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

<b>let </b><font color="Maroon">T</font> be   <a href="ami_1.html#NM8">InsType</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="amistd_2.html#D11">AMISTD_2:def 11</a><br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="122_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:122_1_1_1"/>
( <font color="Maroon">T</font> <a href="hidden.html#R1">=</a> 0 or <font color="Maroon">T</font> <a href="hidden.html#R1">=</a> 1 or <font color="Maroon">T</font> <a href="hidden.html#R1">=</a> 2 or <font color="Maroon">T</font> <a href="hidden.html#R1">=</a> 3 or <font color="Maroon">T</font> <a href="hidden.html#R1">=</a> 4 or <font color="Maroon">T</font> <a href="hidden.html#R1">=</a> 5 or <font color="Maroon">T</font> <a href="hidden.html#R1">=</a> 6 or <font color="Maroon">T</font> <a href="hidden.html#R1">=</a> 7 or <font color="Maroon">T</font> <a href="hidden.html#R1">=</a> 8 or <font color="Maroon">T</font> <a href="hidden.html#R1">=</a> 9 or <font color="Maroon">T</font> <a href="hidden.html#R1">=</a> 10 or <font color="Maroon">T</font> <a href="hidden.html#R1">=</a> 11 or <font color="Maroon">T</font> <a href="hidden.html#R1">=</a> 12 )
 </span><b>by </b><i/>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="122_1_1_1_1"><b>suppose </b></a><a NAME="E1:122_1_1_1_1"/><i><font color="Green">E53</font></i>: 
<font color="Maroon">T</font> <a href="hidden.html#R1">=</a> 0
 ;<br/><div class="add"><b>reconsider </b><font color="Maroon">f</font> =  <a href="xboole_0.html#K1">{}</a>  as   <a href="funct_1.html#NM1">Function</a> ;<br/><b>take </b>
<font color="Maroon">f</font>
; <i><font color="Red">:: according to </font></i><a class="ref" href="amistd_2.html#D2">AMISTD_2:def 2</a><br/><b>thus </b><a NAME="E3:122_1_1_1_1"/>
 <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font> <a href="hidden.html#R1">=</a>  <a href="card_3.html#K4">product</a> <font color="Maroon">f</font>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T24" target="_self">Th24</a>, , <a class="ref" href="card_3.html#T19">CARD_3:19</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="122_1_1_1_2"><b>suppose </b></a><a NAME="E1:122_1_1_1_2"/><i><font color="Green">E64</font></i>: 
<font color="Maroon">T</font> <a href="hidden.html#R1">=</a> 1
 ;<br/><div class="add"><b>take </b>
 <a href="amistd_2.html#K1">PA</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span>
; <i><font color="Red">:: according to </font></i><a class="ref" href="amistd_2.html#D2">AMISTD_2:def 2</a><br/><b>thus </b><a NAME="E2:122_1_1_1_2"/>
 <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font> <a href="tarski.html#R1">c=</a>  <a href="card_3.html#K4">product</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="amistd_2.html#T9">AMISTD_2:9</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><br/><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/><b>assume </b><a NAME="E3:122_1_1_1_2"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="card_3.html#K4">product</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span>
 ;<br/><b>then consider </b><font color="Maroon">f</font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E5:122_1_1_1_2"/><i><font color="Green">E66</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font>
 <b>and </b><br/><a NAME="E6:122_1_1_1_2"/><i><font color="Green">E102</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span>
 <b>and </b><br/><a NAME="E7:122_1_1_1_2"/><i><font color="Green">E103</font></i>: 
for <font color="Olive">k</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">k</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span> holds <br/><font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font>
 <b>by </b><i><a class="ref" href="card_3.html#D5">CARD_3:def 5</a></i>;<br/><a NAME="E8:122_1_1_1_2"/><i><font color="Green">E104</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T24" target="_self">Th24</a>, </i>;<br/><a NAME="E9:122_1_1_1_2"/><b>then </b><i><font color="Green">E105</font></i>: 
1 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><a NAME="E10:122_1_1_1_2"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> 1
 <b>by </b><i><a class="ref" href="scmfsa10.html#T27" target="_self">Th27</a></i>;<br/><a NAME="E11:122_1_1_1_2"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R2">in</a>  <a href="card_3.html#K5">pi</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span>,1
 <b>by </b><i><a class="ref" href="scmfsa10.html#T29" target="_self">Th29</a>, <a class="ref" href="amistd_2.html#D1">AMISTD_2:def 1</a></i>;<br/><b>then consider </b><font color="Maroon">g</font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E13:122_1_1_1_2"/><i><font color="Green">E119</font></i>: 
<font color="Maroon">g</font> <a href="hidden.html#R2">in</a>  <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font>
 <b>and </b><br/><a NAME="E14:122_1_1_1_2"/><i><font color="Green">E130</font></i>: 
<font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1
 <b>by </b><i><a class="ref" href="card_3.html#D6">CARD_3:def 6</a></i>;<br/><a NAME="E15:122_1_1_1_2"/><i><font color="Green">E166</font></i>: 
2 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T28" target="_self">Th28</a>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><a NAME="E16:122_1_1_1_2"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> 2
 <b>by </b><i><a class="ref" href="scmfsa10.html#T27" target="_self">Th27</a></i>;<br/><a NAME="E17:122_1_1_1_2"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R2">in</a>  <a href="card_3.html#K5">pi</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span>,2
 <b>by </b><i><a class="txt" href="scmfsa10.html#E6:122_1_1_1_2"><i><font color="Green">E102</font></i></a>, <a class="ref" href="amistd_2.html#D1">AMISTD_2:def 1</a></i>;<br/><b>then consider </b><font color="Maroon">h</font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E19:122_1_1_1_2"/><i><font color="Green">E167</font></i>: 
<font color="Maroon">h</font> <a href="hidden.html#R2">in</a>  <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font>
 <b>and </b><br/><a NAME="E20:122_1_1_1_2"/><i><font color="Green">E168</font></i>: 
<font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 2
 <b>by </b><i><a class="ref" href="card_3.html#D6">CARD_3:def 6</a></i>;<br/><b>consider </b><font color="Maroon">I</font> being   <a href="ami_1.html#NM3">Instruction</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> <b> such that </b><br/><a NAME="E22:122_1_1_1_2"/><i><font color="Green">E169</font></i>: 
<font color="Maroon">g</font> <a href="hidden.html#R1">=</a>  <a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font>
 <b>and </b><br/><a NAME="E23:122_1_1_1_2"/><i><font color="Green">E170</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Maroon">T</font>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T30" target="_self">Th30</a></i>;<br/><b>consider </b><font color="Maroon">d1</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">b</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> <b> such that </b><br/><a NAME="E25:122_1_1_1_2"/><i><font color="Green">E171</font></i>: 
<font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d1</font> <a href="scmfsa_2.html#K8">:=</a> <font color="Maroon">b</font>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T24" target="_self">Th24</a>, <a class="ref" href="scmfsa10.html#T32" target="_self">Th32</a>, <a class="ref" href="scmfsa_2.html#T54">SCMFSA_2:54</a></i>;<br/><a NAME="E26:122_1_1_1_2"/><i><font color="Green">E172</font></i>: 
<font color="Maroon">g</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">b</font></span><a href="finseq_4.html#K2">*&gt;</a></span>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E9:122_1_1_1_2"><i><font color="Green">E105</font></i></a>, <a class="ref" href="scmfsa10.html#T33" target="_self">Th33</a>, </i>;<br/><b>consider </b><font color="Maroon">J</font> being   <a href="ami_1.html#NM3">Instruction</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> <b> such that </b><br/><a NAME="E28:122_1_1_1_2"/><i><font color="Green">E173</font></i>: 
<font color="Maroon">h</font> <a href="hidden.html#R1">=</a>  <a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">J</font>
 <b>and </b><br/><a NAME="E29:122_1_1_1_2"/><i><font color="Green">E184</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Maroon">T</font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E7:122_1_1_1_2"><i><font color="Green">E103</font></i></a></i>;<br/><b>consider </b><font color="Maroon">a</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">d2</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> <b> such that </b><br/><a NAME="E31:122_1_1_1_2"/><i><font color="Green">E185</font></i>: 
<font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="scmfsa_2.html#K8">:=</a> <font color="Maroon">d2</font>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T24" target="_self">Th24</a>, <a class="ref" href="scmfsa10.html#T36" target="_self">Th36</a>, <a class="ref" href="scmfsa_2.html#T54">SCMFSA_2:54</a></i>;<br/><a NAME="E32:122_1_1_1_2"/><i><font color="Green">E200</font></i>: 
<font color="Maroon">h</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">d2</font></span><a href="finseq_4.html#K2">*&gt;</a></span>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T35" target="_self">Th35</a>, <a class="ref" href="scmfsa10.html#T37" target="_self">Th37</a>, </i>;<br/><a NAME="E33:122_1_1_1_2"/><i><font color="Green">E201</font></i>: 
 <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">d2</font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span>
 <b>by </b><i><a class="ref" href="finseq_1.html#T4">FINSEQ_1:4</a>, <a class="ref" href="finseq_3.html#T29">FINSEQ_3:29</a></i>;<br/><a NAME="E34:122_1_1_1_2"/>
for <font color="Olive">k</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">k</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span> holds <br/><span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">d2</font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="122_1_1_1_2_1"><b>proof </b></a><div class="add">

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

<b>assume </b><a NAME="E1:122_1_1_1_2_1"/><i><font color="Green">E202</font></i>: 
<font color="Maroon">k</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span>
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="122_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="E1:122_1_1_1_2_1_1"/>
( <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 1 or <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 2 )
 </span><b>by </b><i>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="122_1_1_1_2_1_1_1"><b>suppose </b></a><a NAME="E1:122_1_1_1_2_1_1_1"/><i><font color="Green">E203</font></i>: 
<font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 1
 ;<br/><div class="add"><span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">d2</font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="funct_1.html#K1">.</a> 1 = 
<font color="Maroon">d1</font>
<b>by </b><i><a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>
<br/>.= 
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1
<b>by </b><i><a class="ref" href="scmfsa10.html#T31" target="_self">Th31</a>, <a class="ref" href="scmfsa10.html#T34" target="_self">Th34</a>, <a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>
;<br/><b>hence </b><a NAME="E3:122_1_1_1_2_1_1_1"/>
<span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">d2</font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T40" target="_self">Th40</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="122_1_1_1_2_1_1_2"><b>suppose </b></a><a NAME="E1:122_1_1_1_2_1_1_2"/><i><font color="Green">E204</font></i>: 
<font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 2
 ;<br/><div class="add"><span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">d2</font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="funct_1.html#K1">.</a> 2 = 
<font color="Maroon">d2</font>
<b>by </b><i><a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>
<br/>.= 
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 2
<b>by </b><i><a class="txt" href="scmfsa10.html#E8:122_1_1_1_2"><i><font color="Green">E104</font></i></a>, <a class="ref" href="scmfsa10.html#T38" target="_self">Th38</a>, <a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>
;<br/><b>hence </b><a NAME="E3:122_1_1_1_2_1_1_2"/>
<span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">d2</font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T40" target="_self">Th40</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div><a NAME="E35:122_1_1_1_2"/><b>then </b><i><font color="Green">E205</font></i>: 
<span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">d2</font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T26" target="_self">Th26</a>, <a class="ref" href="scmfsa10.html#T28" target="_self">Th28</a>, <a class="ref" href="scmfsa10.html#T39" target="_self">Th39</a>, <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/><a NAME="E36:122_1_1_1_2"/>
(  <a href="ami_5.html#K1">InsCode</a> <span class="p1">(<span class="default"><font color="Maroon">d1</font> <a href="scmfsa_2.html#K8">:=</a> <font color="Maroon">d2</font></span>)</span> <a href="hidden.html#R1">=</a> 1 &amp;  <a href="amistd_2.html#K4">AddressPart</a> <span class="p1">(<span class="default"><font color="Maroon">d1</font> <a href="scmfsa_2.html#K8">:=</a> <font color="Maroon">d2</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">d2</font></span><a href="finseq_4.html#K2">*&gt;</a></span> )
 <b>by </b><i>, <a class="ref" href="scmfsa_2.html#T42">SCMFSA_2:42</a></i>;<br/><b>hence </b><a NAME="E37:122_1_1_1_2"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T24" target="_self">Th24</a>, <a class="ref" href="scmfsa10.html#T25" target="_self">Th25</a>, </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="122_1_1_1_3"><b>suppose </b></a><a NAME="E1:122_1_1_1_3"/><i><font color="Green">E206</font></i>: 
<font color="Maroon">T</font> <a href="hidden.html#R1">=</a> 2
 ;<br/><div class="add"><b>take </b>
 <a href="amistd_2.html#K1">PA</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span>
; <i><font color="Red">:: according to </font></i><a class="ref" href="amistd_2.html#D2">AMISTD_2:def 2</a><br/><b>thus </b><a NAME="E2:122_1_1_1_3"/>
 <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font> <a href="tarski.html#R1">c=</a>  <a href="card_3.html#K4">product</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="amistd_2.html#T9">AMISTD_2:9</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><br/><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/><b>assume </b><a NAME="E3:122_1_1_1_3"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="card_3.html#K4">product</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span>
 ;<br/><b>then consider </b><font color="Maroon">f</font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E5:122_1_1_1_3"/><i><font color="Green">E207</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font>
 <b>and </b><br/><a NAME="E6:122_1_1_1_3"/><i><font color="Green">E208</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span>
 <b>and </b><br/><a NAME="E7:122_1_1_1_3"/><i><font color="Green">E209</font></i>: 
for <font color="Olive">k</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">k</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span> holds <br/><font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font>
 <b>by </b><i><a class="ref" href="card_3.html#D5">CARD_3:def 5</a></i>;<br/><a NAME="E8:122_1_1_1_3"/><i><font color="Green">E210</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T24" target="_self">Th24</a>, </i>;<br/><a NAME="E9:122_1_1_1_3"/><b>then </b><i><font color="Green">E215</font></i>: 
1 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><a NAME="E10:122_1_1_1_3"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> 1
 <b>by </b><i><a class="ref" href="scmfsa10.html#T27" target="_self">Th27</a></i>;<br/><a NAME="E11:122_1_1_1_3"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R2">in</a>  <a href="card_3.html#K5">pi</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span>,1
 <b>by </b><i><a class="ref" href="scmfsa10.html#T29" target="_self">Th29</a>, <a class="ref" href="amistd_2.html#D1">AMISTD_2:def 1</a></i>;<br/><b>then consider </b><font color="Maroon">g</font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E13:122_1_1_1_3"/><i><font color="Green">E216</font></i>: 
<font color="Maroon">g</font> <a href="hidden.html#R2">in</a>  <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font>
 <b>and </b><br/><a NAME="E14:122_1_1_1_3"/><i><font color="Green">E217</font></i>: 
<font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1
 <b>by </b><i><a class="ref" href="card_3.html#D6">CARD_3:def 6</a></i>;<br/><a NAME="E15:122_1_1_1_3"/><i><font color="Green">E218</font></i>: 
2 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T28" target="_self">Th28</a>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><a NAME="E16:122_1_1_1_3"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> 2
 <b>by </b><i><a class="ref" href="scmfsa10.html#T27" target="_self">Th27</a></i>;<br/><a NAME="E17:122_1_1_1_3"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R2">in</a>  <a href="card_3.html#K5">pi</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span>,2
 <b>by </b><i>, <a class="ref" href="amistd_2.html#D1">AMISTD_2:def 1</a></i>;<br/><b>then consider </b><font color="Maroon">h</font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E19:122_1_1_1_3"/><i><font color="Green">E219</font></i>: 
<font color="Maroon">h</font> <a href="hidden.html#R2">in</a>  <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font>
 <b>and </b><br/><a NAME="E20:122_1_1_1_3"/><i><font color="Green">E220</font></i>: 
<font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 2
 <b>by </b><i><a class="ref" href="card_3.html#D6">CARD_3:def 6</a></i>;<br/><b>consider </b><font color="Maroon">I</font> being   <a href="ami_1.html#NM3">Instruction</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> <b> such that </b><br/><a NAME="E22:122_1_1_1_3"/><i><font color="Green">E221</font></i>: 
<font color="Maroon">g</font> <a href="hidden.html#R1">=</a>  <a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font>
 <b>and </b><br/><a NAME="E23:122_1_1_1_3"/><i><font color="Green">E222</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Maroon">T</font>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T30" target="_self">Th30</a></i>;<br/><b>consider </b><font color="Maroon">d1</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">b</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> <b> such that </b><br/><a NAME="E25:122_1_1_1_3"/><i><font color="Green">E223</font></i>: 
<font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K9">AddTo</a> <font color="Maroon">d1</font>,<font color="Maroon">b</font>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T24" target="_self">Th24</a>, <a class="ref" href="scmfsa10.html#T32" target="_self">Th32</a>, <a class="ref" href="scmfsa_2.html#T55">SCMFSA_2:55</a></i>;<br/><a NAME="E26:122_1_1_1_3"/><i><font color="Green">E224</font></i>: 
<font color="Maroon">g</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">b</font></span><a href="finseq_4.html#K2">*&gt;</a></span>
 <b>by </b><i>, <a class="ref" href="scmfsa10.html#T33" target="_self">Th33</a>, </i>;<br/><b>consider </b><font color="Maroon">J</font> being   <a href="ami_1.html#NM3">Instruction</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> <b> such that </b><br/><a NAME="E28:122_1_1_1_3"/><i><font color="Green">E225</font></i>: 
<font color="Maroon">h</font> <a href="hidden.html#R1">=</a>  <a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">J</font>
 <b>and </b><br/><a NAME="E29:122_1_1_1_3"/><i><font color="Green">E226</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Maroon">T</font>
 <b>by </b><i/>;<br/><b>consider </b><font color="Maroon">a</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">d2</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> <b> such that </b><br/><a NAME="E31:122_1_1_1_3"/><i><font color="Green">E227</font></i>: 
<font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K9">AddTo</a> <font color="Maroon">a</font>,<font color="Maroon">d2</font>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T24" target="_self">Th24</a>, <a class="ref" href="scmfsa10.html#T36" target="_self">Th36</a>, <a class="ref" href="scmfsa_2.html#T55">SCMFSA_2:55</a></i>;<br/><a NAME="E32:122_1_1_1_3"/><i><font color="Green">E228</font></i>: 
<font color="Maroon">h</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">d2</font></span><a href="finseq_4.html#K2">*&gt;</a></span>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T35" target="_self">Th35</a>, <a class="ref" href="scmfsa10.html#T37" target="_self">Th37</a>, </i>;<br/><a NAME="E33:122_1_1_1_3"/><i><font color="Green">E229</font></i>: 
 <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">d2</font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span>
 <b>by </b><i><a class="ref" href="finseq_1.html#T4">FINSEQ_1:4</a>, <a class="ref" href="finseq_3.html#T29">FINSEQ_3:29</a></i>;<br/><a NAME="E34:122_1_1_1_3"/>
for <font color="Olive">k</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">k</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span> holds <br/><span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">d2</font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="122_1_1_1_3_1"><b>proof </b></a><div class="add">

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

<b>assume </b><a NAME="E1:122_1_1_1_3_1"/><i><font color="Green">E230</font></i>: 
<font color="Maroon">k</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span>
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="122_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="E1:122_1_1_1_3_1_1"/>
( <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 1 or <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 2 )
 </span><b>by </b><i>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="122_1_1_1_3_1_1_1"><b>suppose </b></a><a NAME="E1:122_1_1_1_3_1_1_1"/><i><font color="Green">E231</font></i>: 
<font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 1
 ;<br/><div class="add"><span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">d2</font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="funct_1.html#K1">.</a> 1 = 
<font color="Maroon">d1</font>
<b>by </b><i><a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>
<br/>.= 
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1
<b>by </b><i><a class="ref" href="scmfsa10.html#T31" target="_self">Th31</a>, <a class="ref" href="scmfsa10.html#T34" target="_self">Th34</a>, <a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>
;<br/><b>hence </b><a NAME="E3:122_1_1_1_3_1_1_1"/>
<span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">d2</font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T40" target="_self">Th40</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="122_1_1_1_3_1_1_2"><b>suppose </b></a><a NAME="E1:122_1_1_1_3_1_1_2"/><i><font color="Green">E232</font></i>: 
<font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 2
 ;<br/><div class="add"><span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">d2</font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="funct_1.html#K1">.</a> 2 = 
<font color="Maroon">d2</font>
<b>by </b><i><a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>
<br/>.= 
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 2
<b>by </b><i>, <a class="ref" href="scmfsa10.html#T38" target="_self">Th38</a>, <a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>
;<br/><b>hence </b><a NAME="E3:122_1_1_1_3_1_1_2"/>
<span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">d2</font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T40" target="_self">Th40</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div><a NAME="E35:122_1_1_1_3"/><b>then </b><i><font color="Green">E233</font></i>: 
<span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">d2</font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T26" target="_self">Th26</a>, <a class="ref" href="scmfsa10.html#T28" target="_self">Th28</a>, <a class="ref" href="scmfsa10.html#T39" target="_self">Th39</a>, <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/><a NAME="E36:122_1_1_1_3"/>
(  <a href="ami_5.html#K1">InsCode</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K9">AddTo</a> <font color="Maroon">d1</font>,<font color="Maroon">d2</font></span>)</span> <a href="hidden.html#R1">=</a> 2 &amp;  <a href="amistd_2.html#K4">AddressPart</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K9">AddTo</a> <font color="Maroon">d1</font>,<font color="Maroon">d2</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">d2</font></span><a href="finseq_4.html#K2">*&gt;</a></span> )
 <b>by </b><i>, <a class="ref" href="scmfsa_2.html#T43">SCMFSA_2:43</a></i>;<br/><b>hence </b><a NAME="E37:122_1_1_1_3"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T24" target="_self">Th24</a>, <a class="ref" href="scmfsa10.html#T25" target="_self">Th25</a>, </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="122_1_1_1_4"><b>suppose </b></a><a NAME="E1:122_1_1_1_4"/><i><font color="Green">E234</font></i>: 
<font color="Maroon">T</font> <a href="hidden.html#R1">=</a> 3
 ;<br/><div class="add"><b>take </b>
 <a href="amistd_2.html#K1">PA</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span>
; <i><font color="Red">:: according to </font></i><a class="ref" href="amistd_2.html#D2">AMISTD_2:def 2</a><br/><b>thus </b><a NAME="E2:122_1_1_1_4"/>
 <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font> <a href="tarski.html#R1">c=</a>  <a href="card_3.html#K4">product</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="amistd_2.html#T9">AMISTD_2:9</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><br/><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/><b>assume </b><a NAME="E3:122_1_1_1_4"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="card_3.html#K4">product</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span>
 ;<br/><b>then consider </b><font color="Maroon">f</font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E5:122_1_1_1_4"/><i><font color="Green">E235</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font>
 <b>and </b><br/><a NAME="E6:122_1_1_1_4"/><i><font color="Green">E236</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span>
 <b>and </b><br/><a NAME="E7:122_1_1_1_4"/><i><font color="Green">E237</font></i>: 
for <font color="Olive">k</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">k</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span> holds <br/><font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font>
 <b>by </b><i><a class="ref" href="card_3.html#D5">CARD_3:def 5</a></i>;<br/><a NAME="E8:122_1_1_1_4"/><i><font color="Green">E238</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T24" target="_self">Th24</a>, </i>;<br/><a NAME="E9:122_1_1_1_4"/><b>then </b><i><font color="Green">E239</font></i>: 
1 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><a NAME="E10:122_1_1_1_4"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> 1
 <b>by </b><i><a class="ref" href="scmfsa10.html#T27" target="_self">Th27</a></i>;<br/><a NAME="E11:122_1_1_1_4"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R2">in</a>  <a href="card_3.html#K5">pi</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span>,1
 <b>by </b><i><a class="ref" href="scmfsa10.html#T29" target="_self">Th29</a>, <a class="ref" href="amistd_2.html#D1">AMISTD_2:def 1</a></i>;<br/><b>then consider </b><font color="Maroon">g</font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E13:122_1_1_1_4"/><i><font color="Green">E240</font></i>: 
<font color="Maroon">g</font> <a href="hidden.html#R2">in</a>  <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font>
 <b>and </b><br/><a NAME="E14:122_1_1_1_4"/><i><font color="Green">E241</font></i>: 
<font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1
 <b>by </b><i><a class="ref" href="card_3.html#D6">CARD_3:def 6</a></i>;<br/><a NAME="E15:122_1_1_1_4"/><i><font color="Green">E242</font></i>: 
2 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T28" target="_self">Th28</a>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><a NAME="E16:122_1_1_1_4"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> 2
 <b>by </b><i><a class="ref" href="scmfsa10.html#T27" target="_self">Th27</a></i>;<br/><a NAME="E17:122_1_1_1_4"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R2">in</a>  <a href="card_3.html#K5">pi</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span>,2
 <b>by </b><i>, <a class="ref" href="amistd_2.html#D1">AMISTD_2:def 1</a></i>;<br/><b>then consider </b><font color="Maroon">h</font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E19:122_1_1_1_4"/><i><font color="Green">E243</font></i>: 
<font color="Maroon">h</font> <a href="hidden.html#R2">in</a>  <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font>
 <b>and </b><br/><a NAME="E20:122_1_1_1_4"/><i><font color="Green">E244</font></i>: 
<font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 2
 <b>by </b><i><a class="ref" href="card_3.html#D6">CARD_3:def 6</a></i>;<br/><b>consider </b><font color="Maroon">I</font> being   <a href="ami_1.html#NM3">Instruction</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> <b> such that </b><br/><a NAME="E22:122_1_1_1_4"/><i><font color="Green">E245</font></i>: 
<font color="Maroon">g</font> <a href="hidden.html#R1">=</a>  <a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font>
 <b>and </b><br/><a NAME="E23:122_1_1_1_4"/><i><font color="Green">E246</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Maroon">T</font>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T30" target="_self">Th30</a></i>;<br/><b>consider </b><font color="Maroon">d1</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">b</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> <b> such that </b><br/><a NAME="E25:122_1_1_1_4"/><i><font color="Green">E247</font></i>: 
<font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K10">SubFrom</a> <font color="Maroon">d1</font>,<font color="Maroon">b</font>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T24" target="_self">Th24</a>, <a class="ref" href="scmfsa10.html#T32" target="_self">Th32</a>, <a class="ref" href="scmfsa_2.html#T56">SCMFSA_2:56</a></i>;<br/><a NAME="E26:122_1_1_1_4"/><i><font color="Green">E248</font></i>: 
<font color="Maroon">g</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">b</font></span><a href="finseq_4.html#K2">*&gt;</a></span>
 <b>by </b><i>, <a class="ref" href="scmfsa10.html#T33" target="_self">Th33</a>, </i>;<br/><b>consider </b><font color="Maroon">J</font> being   <a href="ami_1.html#NM3">Instruction</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> <b> such that </b><br/><a NAME="E28:122_1_1_1_4"/><i><font color="Green">E249</font></i>: 
<font color="Maroon">h</font> <a href="hidden.html#R1">=</a>  <a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">J</font>
 <b>and </b><br/><a NAME="E29:122_1_1_1_4"/><i><font color="Green">E250</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Maroon">T</font>
 <b>by </b><i/>;<br/><b>consider </b><font color="Maroon">a</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">d2</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> <b> such that </b><br/><a NAME="E31:122_1_1_1_4"/><i><font color="Green">E251</font></i>: 
<font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K10">SubFrom</a> <font color="Maroon">a</font>,<font color="Maroon">d2</font>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T24" target="_self">Th24</a>, <a class="ref" href="scmfsa10.html#T36" target="_self">Th36</a>, <a class="ref" href="scmfsa_2.html#T56">SCMFSA_2:56</a></i>;<br/><a NAME="E32:122_1_1_1_4"/><i><font color="Green">E252</font></i>: 
<font color="Maroon">h</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">d2</font></span><a href="finseq_4.html#K2">*&gt;</a></span>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T35" target="_self">Th35</a>, <a class="ref" href="scmfsa10.html#T37" target="_self">Th37</a>, </i>;<br/><a NAME="E33:122_1_1_1_4"/><i><font color="Green">E253</font></i>: 
 <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">d2</font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span>
 <b>by </b><i><a class="ref" href="finseq_1.html#T4">FINSEQ_1:4</a>, <a class="ref" href="finseq_3.html#T29">FINSEQ_3:29</a></i>;<br/><a NAME="E34:122_1_1_1_4"/>
for <font color="Olive">k</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">k</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span> holds <br/><span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">d2</font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="122_1_1_1_4_1"><b>proof </b></a><div class="add">

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

<b>assume </b><a NAME="E1:122_1_1_1_4_1"/><i><font color="Green">E254</font></i>: 
<font color="Maroon">k</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span>
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="122_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="E1:122_1_1_1_4_1_1"/>
( <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 1 or <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 2 )
 </span><b>by </b><i>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="122_1_1_1_4_1_1_1"><b>suppose </b></a><a NAME="E1:122_1_1_1_4_1_1_1"/><i><font color="Green">E255</font></i>: 
<font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 1
 ;<br/><div class="add"><span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">d2</font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="funct_1.html#K1">.</a> 1 = 
<font color="Maroon">d1</font>
<b>by </b><i><a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>
<br/>.= 
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1
<b>by </b><i><a class="ref" href="scmfsa10.html#T31" target="_self">Th31</a>, <a class="ref" href="scmfsa10.html#T34" target="_self">Th34</a>, <a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>
;<br/><b>hence </b><a NAME="E3:122_1_1_1_4_1_1_1"/>
<span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">d2</font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T40" target="_self">Th40</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="122_1_1_1_4_1_1_2"><b>suppose </b></a><a NAME="E1:122_1_1_1_4_1_1_2"/><i><font color="Green">E256</font></i>: 
<font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 2
 ;<br/><div class="add"><span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">d2</font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="funct_1.html#K1">.</a> 2 = 
<font color="Maroon">d2</font>
<b>by </b><i><a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>
<br/>.= 
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 2
<b>by </b><i>, <a class="ref" href="scmfsa10.html#T38" target="_self">Th38</a>, <a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>
;<br/><b>hence </b><a NAME="E3:122_1_1_1_4_1_1_2"/>
<span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">d2</font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T40" target="_self">Th40</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div><a NAME="E35:122_1_1_1_4"/><b>then </b><i><font color="Green">E257</font></i>: 
<span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">d2</font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T26" target="_self">Th26</a>, <a class="ref" href="scmfsa10.html#T28" target="_self">Th28</a>, <a class="ref" href="scmfsa10.html#T39" target="_self">Th39</a>, <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/><a NAME="E36:122_1_1_1_4"/>
(  <a href="ami_5.html#K1">InsCode</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <font color="Maroon">d1</font>,<font color="Maroon">d2</font></span>)</span> <a href="hidden.html#R1">=</a> 3 &amp;  <a href="amistd_2.html#K4">AddressPart</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <font color="Maroon">d1</font>,<font color="Maroon">d2</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">d2</font></span><a href="finseq_4.html#K2">*&gt;</a></span> )
 <b>by </b><i>, <a class="ref" href="scmfsa_2.html#T44">SCMFSA_2:44</a></i>;<br/><b>hence </b><a NAME="E37:122_1_1_1_4"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T24" target="_self">Th24</a>, <a class="ref" href="scmfsa10.html#T25" target="_self">Th25</a>, </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="122_1_1_1_5"><b>suppose </b></a><a NAME="E1:122_1_1_1_5"/><i><font color="Green">E258</font></i>: 
<font color="Maroon">T</font> <a href="hidden.html#R1">=</a> 4
 ;<br/><div class="add"><b>take </b>
 <a href="amistd_2.html#K1">PA</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span>
; <i><font color="Red">:: according to </font></i><a class="ref" href="amistd_2.html#D2">AMISTD_2:def 2</a><br/><b>thus </b><a NAME="E2:122_1_1_1_5"/>
 <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font> <a href="tarski.html#R1">c=</a>  <a href="card_3.html#K4">product</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="amistd_2.html#T9">AMISTD_2:9</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><br/><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/><b>assume </b><a NAME="E3:122_1_1_1_5"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="card_3.html#K4">product</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span>
 ;<br/><b>then consider </b><font color="Maroon">f</font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E5:122_1_1_1_5"/><i><font color="Green">E259</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font>
 <b>and </b><br/><a NAME="E6:122_1_1_1_5"/><i><font color="Green">E260</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span>
 <b>and </b><br/><a NAME="E7:122_1_1_1_5"/><i><font color="Green">E261</font></i>: 
for <font color="Olive">k</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">k</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span> holds <br/><font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font>
 <b>by </b><i><a class="ref" href="card_3.html#D5">CARD_3:def 5</a></i>;<br/><a NAME="E8:122_1_1_1_5"/><i><font color="Green">E262</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T24" target="_self">Th24</a>, </i>;<br/><a NAME="E9:122_1_1_1_5"/><b>then </b><i><font color="Green">E263</font></i>: 
1 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><a NAME="E10:122_1_1_1_5"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> 1
 <b>by </b><i><a class="ref" href="scmfsa10.html#T27" target="_self">Th27</a></i>;<br/><a NAME="E11:122_1_1_1_5"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R2">in</a>  <a href="card_3.html#K5">pi</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span>,1
 <b>by </b><i><a class="ref" href="scmfsa10.html#T29" target="_self">Th29</a>, <a class="ref" href="amistd_2.html#D1">AMISTD_2:def 1</a></i>;<br/><b>then consider </b><font color="Maroon">g</font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E13:122_1_1_1_5"/><i><font color="Green">E265</font></i>: 
<font color="Maroon">g</font> <a href="hidden.html#R2">in</a>  <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font>
 <b>and </b><br/><a NAME="E14:122_1_1_1_5"/><i><font color="Green">E266</font></i>: 
<font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1
 <b>by </b><i><a class="ref" href="card_3.html#D6">CARD_3:def 6</a></i>;<br/><a NAME="E15:122_1_1_1_5"/><i><font color="Green">E267</font></i>: 
2 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T28" target="_self">Th28</a>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><a NAME="E16:122_1_1_1_5"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> 2
 <b>by </b><i><a class="ref" href="scmfsa10.html#T27" target="_self">Th27</a></i>;<br/><a NAME="E17:122_1_1_1_5"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R2">in</a>  <a href="card_3.html#K5">pi</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span>,2
 <b>by </b><i>, <a class="ref" href="amistd_2.html#D1">AMISTD_2:def 1</a></i>;<br/><b>then consider </b><font color="Maroon">h</font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E19:122_1_1_1_5"/><i><font color="Green">E268</font></i>: 
<font color="Maroon">h</font> <a href="hidden.html#R2">in</a>  <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font>
 <b>and </b><br/><a NAME="E20:122_1_1_1_5"/><i><font color="Green">E269</font></i>: 
<font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 2
 <b>by </b><i><a class="ref" href="card_3.html#D6">CARD_3:def 6</a></i>;<br/><b>consider </b><font color="Maroon">I</font> being   <a href="ami_1.html#NM3">Instruction</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> <b> such that </b><br/><a NAME="E22:122_1_1_1_5"/><i><font color="Green">E270</font></i>: 
<font color="Maroon">g</font> <a href="hidden.html#R1">=</a>  <a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font>
 <b>and </b><br/><a NAME="E23:122_1_1_1_5"/><i><font color="Green">E271</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Maroon">T</font>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T30" target="_self">Th30</a></i>;<br/><b>consider </b><font color="Maroon">d1</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">b</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> <b> such that </b><br/><a NAME="E25:122_1_1_1_5"/><i><font color="Green">E272</font></i>: 
<font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K11">MultBy</a> <font color="Maroon">d1</font>,<font color="Maroon">b</font>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T24" target="_self">Th24</a>, <a class="ref" href="scmfsa10.html#T32" target="_self">Th32</a>, <a class="ref" href="scmfsa_2.html#T57">SCMFSA_2:57</a></i>;<br/><a NAME="E26:122_1_1_1_5"/><i><font color="Green">E273</font></i>: 
<font color="Maroon">g</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">b</font></span><a href="finseq_4.html#K2">*&gt;</a></span>
 <b>by </b><i>, <a class="ref" href="scmfsa10.html#T33" target="_self">Th33</a>, </i>;<br/><b>consider </b><font color="Maroon">J</font> being   <a href="ami_1.html#NM3">Instruction</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> <b> such that </b><br/><a NAME="E28:122_1_1_1_5"/><i><font color="Green">E274</font></i>: 
<font color="Maroon">h</font> <a href="hidden.html#R1">=</a>  <a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">J</font>
 <b>and </b><br/><a NAME="E29:122_1_1_1_5"/><i><font color="Green">E275</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Maroon">T</font>
 <b>by </b><i/>;<br/><b>consider </b><font color="Maroon">a</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">d2</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> <b> such that </b><br/><a NAME="E31:122_1_1_1_5"/><i><font color="Green">E276</font></i>: 
<font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K11">MultBy</a> <font color="Maroon">a</font>,<font color="Maroon">d2</font>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T24" target="_self">Th24</a>, <a class="ref" href="scmfsa10.html#T36" target="_self">Th36</a>, <a class="ref" href="scmfsa_2.html#T57">SCMFSA_2:57</a></i>;<br/><a NAME="E32:122_1_1_1_5"/><i><font color="Green">E277</font></i>: 
<font color="Maroon">h</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">d2</font></span><a href="finseq_4.html#K2">*&gt;</a></span>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T35" target="_self">Th35</a>, <a class="ref" href="scmfsa10.html#T37" target="_self">Th37</a>, </i>;<br/><a NAME="E33:122_1_1_1_5"/><i><font color="Green">E278</font></i>: 
 <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">d2</font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span>
 <b>by </b><i><a class="ref" href="finseq_1.html#T4">FINSEQ_1:4</a>, <a class="ref" href="finseq_3.html#T29">FINSEQ_3:29</a></i>;<br/><a NAME="E34:122_1_1_1_5"/>
for <font color="Olive">k</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">k</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span> holds <br/><span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">d2</font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="122_1_1_1_5_1"><b>proof </b></a><div class="add">

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

<b>assume </b><a NAME="E1:122_1_1_1_5_1"/><i><font color="Green">E279</font></i>: 
<font color="Maroon">k</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span>
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="122_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="E1:122_1_1_1_5_1_1"/>
( <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 1 or <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 2 )
 </span><b>by </b><i>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="122_1_1_1_5_1_1_1"><b>suppose </b></a><a NAME="E1:122_1_1_1_5_1_1_1"/><i><font color="Green">E280</font></i>: 
<font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 1
 ;<br/><div class="add"><span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">d2</font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="funct_1.html#K1">.</a> 1 = 
<font color="Maroon">d1</font>
<b>by </b><i><a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>
<br/>.= 
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1
<b>by </b><i><a class="ref" href="scmfsa10.html#T31" target="_self">Th31</a>, <a class="ref" href="scmfsa10.html#T34" target="_self">Th34</a>, <a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>
;<br/><b>hence </b><a NAME="E3:122_1_1_1_5_1_1_1"/>
<span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">d2</font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T40" target="_self">Th40</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="122_1_1_1_5_1_1_2"><b>suppose </b></a><a NAME="E1:122_1_1_1_5_1_1_2"/><i><font color="Green">E281</font></i>: 
<font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 2
 ;<br/><div class="add"><span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">d2</font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="funct_1.html#K1">.</a> 2 = 
<font color="Maroon">d2</font>
<b>by </b><i><a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>
<br/>.= 
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 2
<b>by </b><i>, <a class="ref" href="scmfsa10.html#T38" target="_self">Th38</a>, <a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>
;<br/><b>hence </b><a NAME="E3:122_1_1_1_5_1_1_2"/>
<span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">d2</font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T40" target="_self">Th40</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div><a NAME="E35:122_1_1_1_5"/><b>then </b><i><font color="Green">E282</font></i>: 
<span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">d2</font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T26" target="_self">Th26</a>, <a class="ref" href="scmfsa10.html#T28" target="_self">Th28</a>, <a class="ref" href="scmfsa10.html#T39" target="_self">Th39</a>, <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/><a NAME="E36:122_1_1_1_5"/>
(  <a href="ami_5.html#K1">InsCode</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K11">MultBy</a> <font color="Maroon">d1</font>,<font color="Maroon">d2</font></span>)</span> <a href="hidden.html#R1">=</a> 4 &amp;  <a href="amistd_2.html#K4">AddressPart</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K11">MultBy</a> <font color="Maroon">d1</font>,<font color="Maroon">d2</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">d2</font></span><a href="finseq_4.html#K2">*&gt;</a></span> )
 <b>by </b><i>, <a class="ref" href="scmfsa_2.html#T45">SCMFSA_2:45</a></i>;<br/><b>hence </b><a NAME="E37:122_1_1_1_5"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T24" target="_self">Th24</a>, <a class="ref" href="scmfsa10.html#T25" target="_self">Th25</a>, </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="122_1_1_1_6"><b>suppose </b></a><a NAME="E1:122_1_1_1_6"/><i><font color="Green">E283</font></i>: 
<font color="Maroon">T</font> <a href="hidden.html#R1">=</a> 5
 ;<br/><div class="add"><b>take </b>
 <a href="amistd_2.html#K1">PA</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span>
; <i><font color="Red">:: according to </font></i><a class="ref" href="amistd_2.html#D2">AMISTD_2:def 2</a><br/><b>thus </b><a NAME="E2:122_1_1_1_6"/>
 <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font> <a href="tarski.html#R1">c=</a>  <a href="card_3.html#K4">product</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="amistd_2.html#T9">AMISTD_2:9</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><br/><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/><b>assume </b><a NAME="E3:122_1_1_1_6"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="card_3.html#K4">product</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span>
 ;<br/><b>then consider </b><font color="Maroon">f</font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E5:122_1_1_1_6"/><i><font color="Green">E284</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font>
 <b>and </b><br/><a NAME="E6:122_1_1_1_6"/><i><font color="Green">E285</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span>
 <b>and </b><br/><a NAME="E7:122_1_1_1_6"/><i><font color="Green">E286</font></i>: 
for <font color="Olive">k</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">k</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span> holds <br/><font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font>
 <b>by </b><i><a class="ref" href="card_3.html#D5">CARD_3:def 5</a></i>;<br/><a NAME="E8:122_1_1_1_6"/><i><font color="Green">E287</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T24" target="_self">Th24</a>, </i>;<br/><a NAME="E9:122_1_1_1_6"/><b>then </b><i><font color="Green">E288</font></i>: 
1 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><a NAME="E10:122_1_1_1_6"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> 1
 <b>by </b><i><a class="ref" href="scmfsa10.html#T27" target="_self">Th27</a></i>;<br/><a NAME="E11:122_1_1_1_6"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R2">in</a>  <a href="card_3.html#K5">pi</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span>,1
 <b>by </b><i><a class="ref" href="scmfsa10.html#T29" target="_self">Th29</a>, <a class="ref" href="amistd_2.html#D1">AMISTD_2:def 1</a></i>;<br/><b>then consider </b><font color="Maroon">g</font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E13:122_1_1_1_6"/><i><font color="Green">E289</font></i>: 
<font color="Maroon">g</font> <a href="hidden.html#R2">in</a>  <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font>
 <b>and </b><br/><a NAME="E14:122_1_1_1_6"/><i><font color="Green">E290</font></i>: 
<font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1
 <b>by </b><i><a class="ref" href="card_3.html#D6">CARD_3:def 6</a></i>;<br/><a NAME="E15:122_1_1_1_6"/><i><font color="Green">E291</font></i>: 
2 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T28" target="_self">Th28</a>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><a NAME="E16:122_1_1_1_6"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> 2
 <b>by </b><i><a class="ref" href="scmfsa10.html#T27" target="_self">Th27</a></i>;<br/><a NAME="E17:122_1_1_1_6"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R2">in</a>  <a href="card_3.html#K5">pi</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span>,2
 <b>by </b><i>, <a class="ref" href="amistd_2.html#D1">AMISTD_2:def 1</a></i>;<br/><b>then consider </b><font color="Maroon">h</font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E19:122_1_1_1_6"/><i><font color="Green">E292</font></i>: 
<font color="Maroon">h</font> <a href="hidden.html#R2">in</a>  <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font>
 <b>and </b><br/><a NAME="E20:122_1_1_1_6"/><i><font color="Green">E293</font></i>: 
<font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 2
 <b>by </b><i><a class="ref" href="card_3.html#D6">CARD_3:def 6</a></i>;<br/><b>consider </b><font color="Maroon">I</font> being   <a href="ami_1.html#NM3">Instruction</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> <b> such that </b><br/><a NAME="E22:122_1_1_1_6"/><i><font color="Green">E294</font></i>: 
<font color="Maroon">g</font> <a href="hidden.html#R1">=</a>  <a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font>
 <b>and </b><br/><a NAME="E23:122_1_1_1_6"/><i><font color="Green">E295</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Maroon">T</font>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T30" target="_self">Th30</a></i>;<br/><b>consider </b><font color="Maroon">d1</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">b</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> <b> such that </b><br/><a NAME="E25:122_1_1_1_6"/><i><font color="Green">E296</font></i>: 
<font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K12">Divide</a> <font color="Maroon">d1</font>,<font color="Maroon">b</font>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T24" target="_self">Th24</a>, <a class="ref" href="scmfsa10.html#T32" target="_self">Th32</a>, <a class="ref" href="scmfsa_2.html#T58">SCMFSA_2:58</a></i>;<br/><a NAME="E26:122_1_1_1_6"/><i><font color="Green">E297</font></i>: 
<font color="Maroon">g</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">b</font></span><a href="finseq_4.html#K2">*&gt;</a></span>
 <b>by </b><i>, <a class="ref" href="scmfsa10.html#T33" target="_self">Th33</a>, </i>;<br/><b>consider </b><font color="Maroon">J</font> being   <a href="ami_1.html#NM3">Instruction</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> <b> such that </b><br/><a NAME="E28:122_1_1_1_6"/><i><font color="Green">E298</font></i>: 
<font color="Maroon">h</font> <a href="hidden.html#R1">=</a>  <a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">J</font>
 <b>and </b><br/><a NAME="E29:122_1_1_1_6"/><i><font color="Green">E299</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Maroon">T</font>
 <b>by </b><i/>;<br/><b>consider </b><font color="Maroon">a</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">d2</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> <b> such that </b><br/><a NAME="E31:122_1_1_1_6"/><i><font color="Green">E300</font></i>: 
<font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K12">Divide</a> <font color="Maroon">a</font>,<font color="Maroon">d2</font>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T24" target="_self">Th24</a>, <a class="ref" href="scmfsa10.html#T36" target="_self">Th36</a>, <a class="ref" href="scmfsa_2.html#T58">SCMFSA_2:58</a></i>;<br/><a NAME="E32:122_1_1_1_6"/><i><font color="Green">E301</font></i>: 
<font color="Maroon">h</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">d2</font></span><a href="finseq_4.html#K2">*&gt;</a></span>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T35" target="_self">Th35</a>, <a class="ref" href="scmfsa10.html#T37" target="_self">Th37</a>, </i>;<br/><a NAME="E33:122_1_1_1_6"/><i><font color="Green">E302</font></i>: 
 <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">d2</font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span>
 <b>by </b><i><a class="ref" href="finseq_1.html#T4">FINSEQ_1:4</a>, <a class="ref" href="finseq_3.html#T29">FINSEQ_3:29</a></i>;<br/><a NAME="E34:122_1_1_1_6"/>
for <font color="Olive">k</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">k</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span> holds <br/><span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">d2</font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="122_1_1_1_6_1"><b>proof </b></a><div class="add">

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

<b>assume </b><a NAME="E1:122_1_1_1_6_1"/><i><font color="Green">E303</font></i>: 
<font color="Maroon">k</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span>
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="122_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="E1:122_1_1_1_6_1_1"/>
( <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 1 or <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 2 )
 </span><b>by </b><i>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="122_1_1_1_6_1_1_1"><b>suppose </b></a><a NAME="E1:122_1_1_1_6_1_1_1"/><i><font color="Green">E304</font></i>: 
<font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 1
 ;<br/><div class="add"><span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">d2</font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="funct_1.html#K1">.</a> 1 = 
<font color="Maroon">d1</font>
<b>by </b><i><a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>
<br/>.= 
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1
<b>by </b><i><a class="ref" href="scmfsa10.html#T31" target="_self">Th31</a>, <a class="ref" href="scmfsa10.html#T34" target="_self">Th34</a>, <a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>
;<br/><b>hence </b><a NAME="E3:122_1_1_1_6_1_1_1"/>
<span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">d2</font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T40" target="_self">Th40</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="122_1_1_1_6_1_1_2"><b>suppose </b></a><a NAME="E1:122_1_1_1_6_1_1_2"/><i><font color="Green">E305</font></i>: 
<font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 2
 ;<br/><div class="add"><span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">d2</font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="funct_1.html#K1">.</a> 2 = 
<font color="Maroon">d2</font>
<b>by </b><i><a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>
<br/>.= 
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 2
<b>by </b><i>, <a class="ref" href="scmfsa10.html#T38" target="_self">Th38</a>, <a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>
;<br/><b>hence </b><a NAME="E3:122_1_1_1_6_1_1_2"/>
<span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">d2</font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T40" target="_self">Th40</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div><a NAME="E35:122_1_1_1_6"/><b>then </b><i><font color="Green">E306</font></i>: 
<span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">d2</font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T26" target="_self">Th26</a>, <a class="ref" href="scmfsa10.html#T28" target="_self">Th28</a>, <a class="ref" href="scmfsa10.html#T39" target="_self">Th39</a>, <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/><a NAME="E36:122_1_1_1_6"/>
(  <a href="ami_5.html#K1">InsCode</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K12">Divide</a> <font color="Maroon">d1</font>,<font color="Maroon">d2</font></span>)</span> <a href="hidden.html#R1">=</a> 5 &amp;  <a href="amistd_2.html#K4">AddressPart</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K12">Divide</a> <font color="Maroon">d1</font>,<font color="Maroon">d2</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">d2</font></span><a href="finseq_4.html#K2">*&gt;</a></span> )
 <b>by </b><i>, <a class="ref" href="scmfsa_2.html#T46">SCMFSA_2:46</a></i>;<br/><b>hence </b><a NAME="E37:122_1_1_1_6"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T24" target="_self">Th24</a>, <a class="ref" href="scmfsa10.html#T25" target="_self">Th25</a>, </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="122_1_1_1_7"><b>suppose </b></a><a NAME="E1:122_1_1_1_7"/><i><font color="Green">E307</font></i>: 
<font color="Maroon">T</font> <a href="hidden.html#R1">=</a> 6
 ;<br/><div class="add"><b>take </b>
 <a href="amistd_2.html#K1">PA</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span>
; <i><font color="Red">:: according to </font></i><a class="ref" href="amistd_2.html#D2">AMISTD_2:def 2</a><br/><b>thus </b><a NAME="E2:122_1_1_1_7"/>
 <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font> <a href="tarski.html#R1">c=</a>  <a href="card_3.html#K4">product</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="amistd_2.html#T9">AMISTD_2:9</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><br/><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/><b>assume </b><a NAME="E3:122_1_1_1_7"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="card_3.html#K4">product</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span>
 ;<br/><b>then consider </b><font color="Maroon">f</font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E5:122_1_1_1_7"/><i><font color="Green">E308</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font>
 <b>and </b><br/><a NAME="E6:122_1_1_1_7"/><i><font color="Green">E309</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span>
 <b>and </b><br/><a NAME="E7:122_1_1_1_7"/><i><font color="Green">E310</font></i>: 
for <font color="Olive">k</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">k</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span> holds <br/><font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font>
 <b>by </b><i><a class="ref" href="card_3.html#D5">CARD_3:def 5</a></i>;<br/><a NAME="E8:122_1_1_1_7"/><i><font color="Green">E311</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default">1</span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T24" target="_self">Th24</a>, </i>;<br/><a NAME="E9:122_1_1_1_7"/><b>then </b><i><font color="Green">E312</font></i>: 
1 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><a NAME="E10:122_1_1_1_7"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> 1
 <b>by </b><i><a class="ref" href="scmfsa10.html#T27" target="_self">Th27</a></i>;<br/><a NAME="E11:122_1_1_1_7"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R2">in</a>  <a href="card_3.html#K5">pi</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span>,1
 <b>by </b><i><a class="ref" href="scmfsa10.html#T29" target="_self">Th29</a>, <a class="ref" href="amistd_2.html#D1">AMISTD_2:def 1</a></i>;<br/><b>then consider </b><font color="Maroon">g</font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E13:122_1_1_1_7"/><i><font color="Green">E313</font></i>: 
<font color="Maroon">g</font> <a href="hidden.html#R2">in</a>  <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font>
 <b>and </b><br/><a NAME="E14:122_1_1_1_7"/><i><font color="Green">E314</font></i>: 
<font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1
 <b>by </b><i><a class="ref" href="card_3.html#D6">CARD_3:def 6</a></i>;<br/><b>consider </b><font color="Maroon">I</font> being   <a href="ami_1.html#NM3">Instruction</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> <b> such that </b><br/><a NAME="E16:122_1_1_1_7"/><i><font color="Green">E315</font></i>: 
<font color="Maroon">g</font> <a href="hidden.html#R1">=</a>  <a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font>
 <b>and </b><br/><a NAME="E17:122_1_1_1_7"/><i><font color="Green">E316</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Maroon">T</font>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T30" target="_self">Th30</a></i>;<br/><b>consider </b><font color="Maroon">i1</font> being   <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> <b> such that </b><br/><a NAME="E19:122_1_1_1_7"/><i><font color="Green">E317</font></i>: 
<font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K13">goto</a> <font color="Maroon">i1</font>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T24" target="_self">Th24</a>, , <a class="ref" href="scmfsa_2.html#T59">SCMFSA_2:59</a></i>;<br/><a NAME="E20:122_1_1_1_7"/><i><font color="Green">E318</font></i>: 
 <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">i1</font></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default">1</span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="finseq_1.html#T4">FINSEQ_1:4</a>, <a class="ref" href="finseq_1.html#D8">FINSEQ_1:def 8</a></i>;<br/><a NAME="E21:122_1_1_1_7"/>
for <font color="Olive">k</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">k</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default">1</span><a href="tarski.html#K1">}</a></span> holds <br/><span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">i1</font></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="122_1_1_1_7_1"><b>proof </b></a><div class="add">

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

<b>assume </b><a NAME="E1:122_1_1_1_7_1"/>
<font color="Maroon">k</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default">1</span><a href="tarski.html#K1">}</a></span>
 ;<br/>

<a NAME="E2:122_1_1_1_7_1"/><b>then </b>
<font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 1
 
<b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<b>hence </b><a NAME="E3:122_1_1_1_7_1"/>
<span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">i1</font></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T31" target="_self">Th31</a>, , , </i>;<br/>


</div><b>end;</b></div><a NAME="E22:122_1_1_1_7"/><b>then </b><i><font color="Green">E319</font></i>: 
<span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">i1</font></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T26" target="_self">Th26</a>, <a class="ref" href="scmfsa10.html#T28" target="_self">Th28</a>, , <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/><a NAME="E23:122_1_1_1_7"/>
(  <a href="ami_5.html#K1">InsCode</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K13">goto</a> <font color="Maroon">i1</font></span>)</span> <a href="hidden.html#R1">=</a> 6 &amp;  <a href="amistd_2.html#K4">AddressPart</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K13">goto</a> <font color="Maroon">i1</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">i1</font></span><a href="finseq_1.html#K12">*&gt;</a></span> )
 <b>by </b><i>, <a class="ref" href="scmfsa_2.html#T47">SCMFSA_2:47</a></i>;<br/><b>hence </b><a NAME="E24:122_1_1_1_7"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T24" target="_self">Th24</a>, <a class="ref" href="scmfsa10.html#T25" target="_self">Th25</a>, <a class="ref" href="scmfsa10.html#T32" target="_self">Th32</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="122_1_1_1_8"><b>suppose </b></a><a NAME="E1:122_1_1_1_8"/><i><font color="Green">E320</font></i>: 
<font color="Maroon">T</font> <a href="hidden.html#R1">=</a> 7
 ;<br/><div class="add"><b>take </b>
 <a href="amistd_2.html#K1">PA</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span>
; <i><font color="Red">:: according to </font></i><a class="ref" href="amistd_2.html#D2">AMISTD_2:def 2</a><br/><b>thus </b><a NAME="E2:122_1_1_1_8"/>
 <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font> <a href="tarski.html#R1">c=</a>  <a href="card_3.html#K4">product</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="amistd_2.html#T9">AMISTD_2:9</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><br/><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/><b>assume </b><a NAME="E3:122_1_1_1_8"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="card_3.html#K4">product</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span>
 ;<br/><b>then consider </b><font color="Maroon">f</font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E5:122_1_1_1_8"/><i><font color="Green">E321</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font>
 <b>and </b><br/><a NAME="E6:122_1_1_1_8"/><i><font color="Green">E322</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span>
 <b>and </b><br/><a NAME="E7:122_1_1_1_8"/><i><font color="Green">E323</font></i>: 
for <font color="Olive">k</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">k</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span> holds <br/><font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font>
 <b>by </b><i><a class="ref" href="card_3.html#D5">CARD_3:def 5</a></i>;<br/><a NAME="E8:122_1_1_1_8"/><i><font color="Green">E324</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T24" target="_self">Th24</a>, </i>;<br/><a NAME="E9:122_1_1_1_8"/><b>then </b><i><font color="Green">E325</font></i>: 
1 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><a NAME="E10:122_1_1_1_8"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> 1
 <b>by </b><i><a class="ref" href="scmfsa10.html#T27" target="_self">Th27</a></i>;<br/><a NAME="E11:122_1_1_1_8"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R2">in</a>  <a href="card_3.html#K5">pi</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span>,1
 <b>by </b><i><a class="ref" href="scmfsa10.html#T29" target="_self">Th29</a>, <a class="ref" href="amistd_2.html#D1">AMISTD_2:def 1</a></i>;<br/><b>then consider </b><font color="Maroon">g</font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E13:122_1_1_1_8"/><i><font color="Green">E326</font></i>: 
<font color="Maroon">g</font> <a href="hidden.html#R2">in</a>  <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font>
 <b>and </b><br/><a NAME="E14:122_1_1_1_8"/><i><font color="Green">E327</font></i>: 
<font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1
 <b>by </b><i><a class="ref" href="card_3.html#D6">CARD_3:def 6</a></i>;<br/><a NAME="E15:122_1_1_1_8"/><i><font color="Green">E328</font></i>: 
2 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T28" target="_self">Th28</a>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><a NAME="E16:122_1_1_1_8"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> 2
 <b>by </b><i><a class="ref" href="scmfsa10.html#T27" target="_self">Th27</a></i>;<br/><a NAME="E17:122_1_1_1_8"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R2">in</a>  <a href="card_3.html#K5">pi</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span>,2
 <b>by </b><i>, <a class="ref" href="amistd_2.html#D1">AMISTD_2:def 1</a></i>;<br/><b>then consider </b><font color="Maroon">h</font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E19:122_1_1_1_8"/><i><font color="Green">E329</font></i>: 
<font color="Maroon">h</font> <a href="hidden.html#R2">in</a>  <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font>
 <b>and </b><br/><a NAME="E20:122_1_1_1_8"/><i><font color="Green">E330</font></i>: 
<font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 2
 <b>by </b><i><a class="ref" href="card_3.html#D6">CARD_3:def 6</a></i>;<br/><b>consider </b><font color="Maroon">I</font> being   <a href="ami_1.html#NM3">Instruction</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> <b> such that </b><br/><a NAME="E22:122_1_1_1_8"/><i><font color="Green">E331</font></i>: 
<font color="Maroon">g</font> <a href="hidden.html#R1">=</a>  <a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font>
 <b>and </b><br/><a NAME="E23:122_1_1_1_8"/><i><font color="Green">E332</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Maroon">T</font>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T30" target="_self">Th30</a></i>;<br/><b>consider </b><font color="Maroon">i1</font> being   <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> , <font color="Maroon">d1</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> <b> such that </b><br/><a NAME="E25:122_1_1_1_8"/><i><font color="Green">E333</font></i>: 
<font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d1</font> <a href="scmfsa_2.html#K14">=0_goto</a> <font color="Maroon">i1</font>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T24" target="_self">Th24</a>, <a class="ref" href="scmfsa10.html#T32" target="_self">Th32</a>, <a class="ref" href="scmfsa_2.html#T60">SCMFSA_2:60</a></i>;<br/><a NAME="E26:122_1_1_1_8"/><i><font color="Green">E334</font></i>: 
<font color="Maroon">g</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">i1</font>,<font color="Maroon">d1</font></span><a href="finseq_4.html#K2">*&gt;</a></span>
 <b>by </b><i>, <a class="ref" href="scmfsa10.html#T33" target="_self">Th33</a>, </i>;<br/><b>consider </b><font color="Maroon">J</font> being   <a href="ami_1.html#NM3">Instruction</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> <b> such that </b><br/><a NAME="E28:122_1_1_1_8"/><i><font color="Green">E335</font></i>: 
<font color="Maroon">h</font> <a href="hidden.html#R1">=</a>  <a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">J</font>
 <b>and </b><br/><a NAME="E29:122_1_1_1_8"/><i><font color="Green">E336</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Maroon">T</font>
 <b>by </b><i/>;<br/><b>consider </b><font color="Maroon">i2</font> being   <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> , <font color="Maroon">d2</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> <b> such that </b><br/><a NAME="E31:122_1_1_1_8"/><i><font color="Green">E337</font></i>: 
<font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d2</font> <a href="scmfsa_2.html#K14">=0_goto</a> <font color="Maroon">i2</font>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T24" target="_self">Th24</a>, <a class="ref" href="scmfsa10.html#T36" target="_self">Th36</a>, <a class="ref" href="scmfsa_2.html#T60">SCMFSA_2:60</a></i>;<br/><a NAME="E32:122_1_1_1_8"/><i><font color="Green">E338</font></i>: 
<font color="Maroon">h</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">i2</font>,<font color="Maroon">d2</font></span><a href="finseq_4.html#K2">*&gt;</a></span>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T35" target="_self">Th35</a>, <a class="ref" href="scmfsa10.html#T37" target="_self">Th37</a>, </i>;<br/><a NAME="E33:122_1_1_1_8"/><i><font color="Green">E339</font></i>: 
 <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">i1</font>,<font color="Maroon">d2</font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span>
 <b>by </b><i><a class="ref" href="finseq_1.html#T4">FINSEQ_1:4</a>, <a class="ref" href="finseq_3.html#T29">FINSEQ_3:29</a></i>;<br/><a NAME="E34:122_1_1_1_8"/>
for <font color="Olive">k</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">k</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span> holds <br/><span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">i1</font>,<font color="Maroon">d2</font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="122_1_1_1_8_1"><b>proof </b></a><div class="add">

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

<b>assume </b><a NAME="E1:122_1_1_1_8_1"/><i><font color="Green">E340</font></i>: 
<font color="Maroon">k</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span>
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="122_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="E1:122_1_1_1_8_1_1"/>
( <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 1 or <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 2 )
 </span><b>by </b><i>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="122_1_1_1_8_1_1_1"><b>suppose </b></a><a NAME="E1:122_1_1_1_8_1_1_1"/><i><font color="Green">E341</font></i>: 
<font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 1
 ;<br/><div class="add"><span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">i1</font>,<font color="Maroon">d2</font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="funct_1.html#K1">.</a> 1 = 
<font color="Maroon">i1</font>
<b>by </b><i><a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>
<br/>.= 
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1
<b>by </b><i><a class="ref" href="scmfsa10.html#T31" target="_self">Th31</a>, <a class="ref" href="scmfsa10.html#T34" target="_self">Th34</a>, <a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>
;<br/><b>hence </b><a NAME="E3:122_1_1_1_8_1_1_1"/>
<span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">i1</font>,<font color="Maroon">d2</font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T40" target="_self">Th40</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="122_1_1_1_8_1_1_2"><b>suppose </b></a><a NAME="E1:122_1_1_1_8_1_1_2"/><i><font color="Green">E342</font></i>: 
<font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 2
 ;<br/><div class="add"><span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">i1</font>,<font color="Maroon">d2</font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="funct_1.html#K1">.</a> 2 = 
<font color="Maroon">d2</font>
<b>by </b><i><a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>
<br/>.= 
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 2
<b>by </b><i>, <a class="ref" href="scmfsa10.html#T38" target="_self">Th38</a>, <a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>
;<br/><b>hence </b><a NAME="E3:122_1_1_1_8_1_1_2"/>
<span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">i1</font>,<font color="Maroon">d2</font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T40" target="_self">Th40</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div><a NAME="E35:122_1_1_1_8"/><b>then </b><i><font color="Green">E343</font></i>: 
<span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">i1</font>,<font color="Maroon">d2</font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T26" target="_self">Th26</a>, <a class="ref" href="scmfsa10.html#T28" target="_self">Th28</a>, <a class="ref" href="scmfsa10.html#T39" target="_self">Th39</a>, <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/><a NAME="E36:122_1_1_1_8"/>
(  <a href="ami_5.html#K1">InsCode</a> <span class="p1">(<span class="default"><font color="Maroon">d2</font> <a href="scmfsa_2.html#K14">=0_goto</a> <font color="Maroon">i1</font></span>)</span> <a href="hidden.html#R1">=</a> 7 &amp;  <a href="amistd_2.html#K4">AddressPart</a> <span class="p1">(<span class="default"><font color="Maroon">d2</font> <a href="scmfsa_2.html#K14">=0_goto</a> <font color="Maroon">i1</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">i1</font>,<font color="Maroon">d2</font></span><a href="finseq_4.html#K2">*&gt;</a></span> )
 <b>by </b><i>, <a class="ref" href="scmfsa_2.html#T48">SCMFSA_2:48</a></i>;<br/><b>hence </b><a NAME="E37:122_1_1_1_8"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T24" target="_self">Th24</a>, <a class="ref" href="scmfsa10.html#T25" target="_self">Th25</a>, </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="122_1_1_1_9"><b>suppose </b></a><a NAME="E1:122_1_1_1_9"/><i><font color="Green">E344</font></i>: 
<font color="Maroon">T</font> <a href="hidden.html#R1">=</a> 8
 ;<br/><div class="add"><b>take </b>
 <a href="amistd_2.html#K1">PA</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span>
; <i><font color="Red">:: according to </font></i><a class="ref" href="amistd_2.html#D2">AMISTD_2:def 2</a><br/><b>thus </b><a NAME="E2:122_1_1_1_9"/>
 <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font> <a href="tarski.html#R1">c=</a>  <a href="card_3.html#K4">product</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="amistd_2.html#T9">AMISTD_2:9</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><br/><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/><b>assume </b><a NAME="E3:122_1_1_1_9"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="card_3.html#K4">product</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span>
 ;<br/><b>then consider </b><font color="Maroon">f</font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E5:122_1_1_1_9"/><i><font color="Green">E345</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font>
 <b>and </b><br/><a NAME="E6:122_1_1_1_9"/><i><font color="Green">E346</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span>
 <b>and </b><br/><a NAME="E7:122_1_1_1_9"/><i><font color="Green">E347</font></i>: 
for <font color="Olive">k</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">k</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span> holds <br/><font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font>
 <b>by </b><i><a class="ref" href="card_3.html#D5">CARD_3:def 5</a></i>;<br/><a NAME="E8:122_1_1_1_9"/><i><font color="Green">E348</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T24" target="_self">Th24</a>, </i>;<br/><a NAME="E9:122_1_1_1_9"/><b>then </b><i><font color="Green">E349</font></i>: 
1 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><a NAME="E10:122_1_1_1_9"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> 1
 <b>by </b><i><a class="ref" href="scmfsa10.html#T27" target="_self">Th27</a></i>;<br/><a NAME="E11:122_1_1_1_9"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R2">in</a>  <a href="card_3.html#K5">pi</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span>,1
 <b>by </b><i><a class="ref" href="scmfsa10.html#T29" target="_self">Th29</a>, <a class="ref" href="amistd_2.html#D1">AMISTD_2:def 1</a></i>;<br/><b>then consider </b><font color="Maroon">g</font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E13:122_1_1_1_9"/><i><font color="Green">E350</font></i>: 
<font color="Maroon">g</font> <a href="hidden.html#R2">in</a>  <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font>
 <b>and </b><br/><a NAME="E14:122_1_1_1_9"/><i><font color="Green">E351</font></i>: 
<font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1
 <b>by </b><i><a class="ref" href="card_3.html#D6">CARD_3:def 6</a></i>;<br/><a NAME="E15:122_1_1_1_9"/><i><font color="Green">E352</font></i>: 
2 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T28" target="_self">Th28</a>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><a NAME="E16:122_1_1_1_9"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> 2
 <b>by </b><i><a class="ref" href="scmfsa10.html#T27" target="_self">Th27</a></i>;<br/><a NAME="E17:122_1_1_1_9"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R2">in</a>  <a href="card_3.html#K5">pi</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span>,2
 <b>by </b><i>, <a class="ref" href="amistd_2.html#D1">AMISTD_2:def 1</a></i>;<br/><b>then consider </b><font color="Maroon">h</font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E19:122_1_1_1_9"/><i><font color="Green">E353</font></i>: 
<font color="Maroon">h</font> <a href="hidden.html#R2">in</a>  <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font>
 <b>and </b><br/><a NAME="E20:122_1_1_1_9"/><i><font color="Green">E354</font></i>: 
<font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 2
 <b>by </b><i><a class="ref" href="card_3.html#D6">CARD_3:def 6</a></i>;<br/><b>consider </b><font color="Maroon">I</font> being   <a href="ami_1.html#NM3">Instruction</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> <b> such that </b><br/><a NAME="E22:122_1_1_1_9"/><i><font color="Green">E355</font></i>: 
<font color="Maroon">g</font> <a href="hidden.html#R1">=</a>  <a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font>
 <b>and </b><br/><a NAME="E23:122_1_1_1_9"/><i><font color="Green">E356</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Maroon">T</font>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T30" target="_self">Th30</a></i>;<br/><b>consider </b><font color="Maroon">i1</font> being   <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> , <font color="Maroon">d1</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> <b> such that </b><br/><a NAME="E25:122_1_1_1_9"/><i><font color="Green">E357</font></i>: 
<font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d1</font> <a href="scmfsa_2.html#K15">&gt;0_goto</a> <font color="Maroon">i1</font>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T24" target="_self">Th24</a>, <a class="ref" href="scmfsa10.html#T32" target="_self">Th32</a>, <a class="ref" href="scmfsa_2.html#T61">SCMFSA_2:61</a></i>;<br/><a NAME="E26:122_1_1_1_9"/><i><font color="Green">E358</font></i>: 
<font color="Maroon">g</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">i1</font>,<font color="Maroon">d1</font></span><a href="finseq_4.html#K2">*&gt;</a></span>
 <b>by </b><i>, <a class="ref" href="scmfsa10.html#T33" target="_self">Th33</a>, </i>;<br/><b>consider </b><font color="Maroon">J</font> being   <a href="ami_1.html#NM3">Instruction</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> <b> such that </b><br/><a NAME="E28:122_1_1_1_9"/><i><font color="Green">E359</font></i>: 
<font color="Maroon">h</font> <a href="hidden.html#R1">=</a>  <a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">J</font>
 <b>and </b><br/><a NAME="E29:122_1_1_1_9"/><i><font color="Green">E360</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Maroon">T</font>
 <b>by </b><i/>;<br/><b>consider </b><font color="Maroon">i2</font> being   <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> , <font color="Maroon">d2</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> <b> such that </b><br/><a NAME="E31:122_1_1_1_9"/><i><font color="Green">E361</font></i>: 
<font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d2</font> <a href="scmfsa_2.html#K15">&gt;0_goto</a> <font color="Maroon">i2</font>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T24" target="_self">Th24</a>, <a class="ref" href="scmfsa10.html#T36" target="_self">Th36</a>, <a class="ref" href="scmfsa_2.html#T61">SCMFSA_2:61</a></i>;<br/><a NAME="E32:122_1_1_1_9"/><i><font color="Green">E362</font></i>: 
<font color="Maroon">h</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">i2</font>,<font color="Maroon">d2</font></span><a href="finseq_4.html#K2">*&gt;</a></span>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T35" target="_self">Th35</a>, <a class="ref" href="scmfsa10.html#T37" target="_self">Th37</a>, </i>;<br/><a NAME="E33:122_1_1_1_9"/><i><font color="Green">E363</font></i>: 
 <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">i1</font>,<font color="Maroon">d2</font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span>
 <b>by </b><i><a class="ref" href="finseq_1.html#T4">FINSEQ_1:4</a>, <a class="ref" href="finseq_3.html#T29">FINSEQ_3:29</a></i>;<br/><a NAME="E34:122_1_1_1_9"/>
for <font color="Olive">k</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">k</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span> holds <br/><span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">i1</font>,<font color="Maroon">d2</font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="122_1_1_1_9_1"><b>proof </b></a><div class="add">

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

<b>assume </b><a NAME="E1:122_1_1_1_9_1"/><i><font color="Green">E364</font></i>: 
<font color="Maroon">k</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span>
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="122_1_1_1_9_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:122_1_1_1_9_1_1"/>
( <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 1 or <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 2 )
 </span><b>by </b><i>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="122_1_1_1_9_1_1_1"><b>suppose </b></a><a NAME="E1:122_1_1_1_9_1_1_1"/><i><font color="Green">E365</font></i>: 
<font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 1
 ;<br/><div class="add"><span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">i1</font>,<font color="Maroon">d2</font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="funct_1.html#K1">.</a> 1 = 
<font color="Maroon">i1</font>
<b>by </b><i><a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>
<br/>.= 
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1
<b>by </b><i><a class="ref" href="scmfsa10.html#T31" target="_self">Th31</a>, <a class="ref" href="scmfsa10.html#T34" target="_self">Th34</a>, <a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>
;<br/><b>hence </b><a NAME="E3:122_1_1_1_9_1_1_1"/>
<span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">i1</font>,<font color="Maroon">d2</font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T40" target="_self">Th40</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="122_1_1_1_9_1_1_2"><b>suppose </b></a><a NAME="E1:122_1_1_1_9_1_1_2"/><i><font color="Green">E366</font></i>: 
<font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 2
 ;<br/><div class="add"><span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">i1</font>,<font color="Maroon">d2</font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="funct_1.html#K1">.</a> 2 = 
<font color="Maroon">d2</font>
<b>by </b><i><a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>
<br/>.= 
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 2
<b>by </b><i>, <a class="ref" href="scmfsa10.html#T38" target="_self">Th38</a>, <a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>
;<br/><b>hence </b><a NAME="E3:122_1_1_1_9_1_1_2"/>
<span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">i1</font>,<font color="Maroon">d2</font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T40" target="_self">Th40</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div><a NAME="E35:122_1_1_1_9"/><b>then </b><i><font color="Green">E367</font></i>: 
<span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">i1</font>,<font color="Maroon">d2</font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T26" target="_self">Th26</a>, <a class="ref" href="scmfsa10.html#T28" target="_self">Th28</a>, <a class="ref" href="scmfsa10.html#T39" target="_self">Th39</a>, <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/><a NAME="E36:122_1_1_1_9"/>
(  <a href="ami_5.html#K1">InsCode</a> <span class="p1">(<span class="default"><font color="Maroon">d2</font> <a href="scmfsa_2.html#K15">&gt;0_goto</a> <font color="Maroon">i1</font></span>)</span> <a href="hidden.html#R1">=</a> 8 &amp;  <a href="amistd_2.html#K4">AddressPart</a> <span class="p1">(<span class="default"><font color="Maroon">d2</font> <a href="scmfsa_2.html#K15">&gt;0_goto</a> <font color="Maroon">i1</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">i1</font>,<font color="Maroon">d2</font></span><a href="finseq_4.html#K2">*&gt;</a></span> )
 <b>by </b><i>, <a class="ref" href="scmfsa_2.html#T49">SCMFSA_2:49</a></i>;<br/><b>hence </b><a NAME="E37:122_1_1_1_9"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T24" target="_self">Th24</a>, <a class="ref" href="scmfsa10.html#T25" target="_self">Th25</a>, </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="122_1_1_1_10"><b>suppose </b></a><a NAME="E1:122_1_1_1_10"/><i><font color="Green">E368</font></i>: 
<font color="Maroon">T</font> <a href="hidden.html#R1">=</a> 9
 ;<br/><div class="add"><b>take </b>
 <a href="amistd_2.html#K1">PA</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span>
; <i><font color="Red">:: according to </font></i><a class="ref" href="amistd_2.html#D2">AMISTD_2:def 2</a><br/><b>thus </b><a NAME="E2:122_1_1_1_10"/>
 <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font> <a href="tarski.html#R1">c=</a>  <a href="card_3.html#K4">product</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="amistd_2.html#T9">AMISTD_2:9</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><br/><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/><b>assume </b><a NAME="E3:122_1_1_1_10"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="card_3.html#K4">product</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span>
 ;<br/><b>then consider </b><font color="Maroon">f</font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E5:122_1_1_1_10"/><i><font color="Green">E369</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font>
 <b>and </b><br/><a NAME="E6:122_1_1_1_10"/><i><font color="Green">E370</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span>
 <b>and </b><br/><a NAME="E7:122_1_1_1_10"/><i><font color="Green">E371</font></i>: 
for <font color="Olive">k</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">k</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span> holds <br/><font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font>
 <b>by </b><i><a class="ref" href="card_3.html#D5">CARD_3:def 5</a></i>;<br/><a NAME="E8:122_1_1_1_10"/><i><font color="Green">E372</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="enumset1.html#K1">{</a><span class="default">1,2,3</span><a href="enumset1.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T24" target="_self">Th24</a>, </i>;<br/><a NAME="E9:122_1_1_1_10"/><b>then </b><i><font color="Green">E373</font></i>: 
1 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="enumset1.html#D1">ENUMSET1:def 1</a></i>;<br/><a NAME="E10:122_1_1_1_10"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> 1
 <b>by </b><i><a class="ref" href="scmfsa10.html#T27" target="_self">Th27</a></i>;<br/><a NAME="E11:122_1_1_1_10"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R2">in</a>  <a href="card_3.html#K5">pi</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span>,1
 <b>by </b><i><a class="ref" href="scmfsa10.html#T29" target="_self">Th29</a>, <a class="ref" href="amistd_2.html#D1">AMISTD_2:def 1</a></i>;<br/><b>then consider </b><font color="Maroon">g</font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E13:122_1_1_1_10"/><i><font color="Green">E374</font></i>: 
<font color="Maroon">g</font> <a href="hidden.html#R2">in</a>  <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font>
 <b>and </b><br/><a NAME="E14:122_1_1_1_10"/><i><font color="Green">E375</font></i>: 
<font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1
 <b>by </b><i><a class="ref" href="card_3.html#D6">CARD_3:def 6</a></i>;<br/><a NAME="E15:122_1_1_1_10"/><i><font color="Green">E376</font></i>: 
2 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T28" target="_self">Th28</a>, <a class="ref" href="enumset1.html#D1">ENUMSET1:def 1</a></i>;<br/><a NAME="E16:122_1_1_1_10"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> 2
 <b>by </b><i><a class="ref" href="scmfsa10.html#T27" target="_self">Th27</a></i>;<br/><a NAME="E17:122_1_1_1_10"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R2">in</a>  <a href="card_3.html#K5">pi</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span>,2
 <b>by </b><i>, <a class="ref" href="amistd_2.html#D1">AMISTD_2:def 1</a></i>;<br/><b>then consider </b><font color="Maroon">h</font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E19:122_1_1_1_10"/><i><font color="Green">E377</font></i>: 
<font color="Maroon">h</font> <a href="hidden.html#R2">in</a>  <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font>
 <b>and </b><br/><a NAME="E20:122_1_1_1_10"/><i><font color="Green">E378</font></i>: 
<font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 2
 <b>by </b><i><a class="ref" href="card_3.html#D6">CARD_3:def 6</a></i>;<br/><a NAME="E21:122_1_1_1_10"/><i><font color="Green">E379</font></i>: 
3 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T28" target="_self">Th28</a>, <a class="ref" href="enumset1.html#D1">ENUMSET1:def 1</a></i>;<br/><a NAME="E22:122_1_1_1_10"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 3 <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> 3
 <b>by </b><i><a class="ref" href="scmfsa10.html#T27" target="_self">Th27</a></i>;<br/><a NAME="E23:122_1_1_1_10"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 3 <a href="hidden.html#R2">in</a>  <a href="card_3.html#K5">pi</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span>,3
 <b>by </b><i>, <a class="ref" href="amistd_2.html#D1">AMISTD_2:def 1</a></i>;<br/><b>then consider </b><font color="Maroon">z</font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E25:122_1_1_1_10"/><i><font color="Green">E380</font></i>: 
<font color="Maroon">z</font> <a href="hidden.html#R2">in</a>  <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font>
 <b>and </b><br/><a NAME="E26:122_1_1_1_10"/><i><font color="Green">E381</font></i>: 
<font color="Maroon">z</font> <a href="funct_1.html#K1">.</a> 3 <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 3
 <b>by </b><i><a class="ref" href="card_3.html#D6">CARD_3:def 6</a></i>;<br/><b>consider </b><font color="Maroon">I</font> being   <a href="ami_1.html#NM3">Instruction</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> <b> such that </b><br/><a NAME="E28:122_1_1_1_10"/><i><font color="Green">E382</font></i>: 
<font color="Maroon">g</font> <a href="hidden.html#R1">=</a>  <a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font>
 <b>and </b><br/><a NAME="E29:122_1_1_1_10"/><i><font color="Green">E383</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Maroon">T</font>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T30" target="_self">Th30</a></i>;<br/><b>consider </b><font color="Maroon">a</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">b</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">f1</font> being    <a href="scmfsa_2.html#M2">FinSeq-Location</a> <b> such that </b><br/><a NAME="E31:122_1_1_1_10"/><i><font color="Green">E384</font></i>: 
<font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> <a href="scmfsa_2.html#K16">:=</a> <font color="Maroon">f1</font>,<font color="Maroon">a</font>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T24" target="_self">Th24</a>, <a class="ref" href="scmfsa10.html#T35" target="_self">Th35</a>, <a class="ref" href="scmfsa_2.html#T62">SCMFSA_2:62</a></i>;<br/><a NAME="E32:122_1_1_1_10"/><i><font color="Green">E385</font></i>: 
<font color="Maroon">g</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><font color="Maroon">b</font>,<font color="Maroon">f1</font>,<font color="Maroon">a</font></span><a href="finseq_4.html#K3">*&gt;</a></span>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T34" target="_self">Th34</a>, <a class="ref" href="scmfsa10.html#T36" target="_self">Th36</a>, </i>;<br/><b>consider </b><font color="Maroon">J</font> being   <a href="ami_1.html#NM3">Instruction</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> <b> such that </b><br/><a NAME="E34:122_1_1_1_10"/><i><font color="Green">E386</font></i>: 
<font color="Maroon">h</font> <a href="hidden.html#R1">=</a>  <a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">J</font>
 <b>and </b><br/><a NAME="E35:122_1_1_1_10"/><i><font color="Green">E387</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Maroon">T</font>
 <b>by </b><i/>;<br/><b>consider </b><font color="Maroon">d1</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">d2</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">f2</font> being    <a href="scmfsa_2.html#M2">FinSeq-Location</a> <b> such that </b><br/><a NAME="E37:122_1_1_1_10"/><i><font color="Green">E388</font></i>: 
<font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d2</font> <a href="scmfsa_2.html#K16">:=</a> <font color="Maroon">f2</font>,<font color="Maroon">d1</font>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T24" target="_self">Th24</a>, <a class="ref" href="scmfsa10.html#T39" target="_self">Th39</a>, <a class="ref" href="scmfsa_2.html#T62">SCMFSA_2:62</a></i>;<br/><a NAME="E38:122_1_1_1_10"/><i><font color="Green">E389</font></i>: 
<font color="Maroon">h</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><font color="Maroon">d2</font>,<font color="Maroon">f2</font>,<font color="Maroon">d1</font></span><a href="finseq_4.html#K3">*&gt;</a></span>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T38" target="_self">Th38</a>, , </i>;<br/><b>consider </b><font color="Maroon">K</font> being   <a href="ami_1.html#NM3">Instruction</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> <b> such that </b><br/><a NAME="E40:122_1_1_1_10"/><i><font color="Green">E391</font></i>: 
<font color="Maroon">z</font> <a href="hidden.html#R1">=</a>  <a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">K</font>
 <b>and </b><br/><a NAME="E41:122_1_1_1_10"/><i><font color="Green">E392</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">K</font> <a href="hidden.html#R1">=</a> <font color="Maroon">T</font>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T32" target="_self">Th32</a></i>;<br/><b>consider </b><font color="Maroon">d3</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">d4</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">f3</font> being    <a href="scmfsa_2.html#M2">FinSeq-Location</a> <b> such that </b><br/><a NAME="E43:122_1_1_1_10"/><i><font color="Green">E393</font></i>: 
<font color="Maroon">K</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d4</font> <a href="scmfsa_2.html#K16">:=</a> <font color="Maroon">f3</font>,<font color="Maroon">d3</font>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T24" target="_self">Th24</a>, <a class="ref" href="scmfsa10.html#T42" target="_self">Th42</a>, <a class="ref" href="scmfsa_2.html#T62">SCMFSA_2:62</a></i>;<br/><a NAME="E44:122_1_1_1_10"/><i><font color="Green">E394</font></i>: 
<font color="Maroon">z</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><font color="Maroon">d4</font>,<font color="Maroon">f3</font>,<font color="Maroon">d3</font></span><a href="finseq_4.html#K3">*&gt;</a></span>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T41" target="_self">Th41</a>, <a class="ref" href="scmfsa10.html#T43" target="_self">Th43</a>, </i>;<br/><a NAME="E45:122_1_1_1_10"/><i><font color="Green">E395</font></i>: 
 <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><font color="Maroon">b</font>,<font color="Maroon">f2</font>,<font color="Maroon">d3</font></span><a href="finseq_4.html#K3">*&gt;</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="enumset1.html#K1">{</a><span class="default">1,2,3</span><a href="enumset1.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="finseq_3.html#T1">FINSEQ_3:1</a>, <a class="ref" href="finseq_3.html#T30">FINSEQ_3:30</a></i>;<br/><a NAME="E46:122_1_1_1_10"/>
for <font color="Olive">k</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">k</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="enumset1.html#K1">{</a><span class="default">1,2,3</span><a href="enumset1.html#K1">}</a></span> holds <br/><span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><font color="Maroon">b</font>,<font color="Maroon">f2</font>,<font color="Maroon">d3</font></span><a href="finseq_4.html#K3">*&gt;</a></span> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="122_1_1_1_10_1"><b>proof </b></a><div class="add">

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

<b>assume </b><a NAME="E1:122_1_1_1_10_1"/><i><font color="Green">E396</font></i>: 
<font color="Maroon">k</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="enumset1.html#K1">{</a><span class="default">1,2,3</span><a href="enumset1.html#K1">}</a></span>
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="122_1_1_1_10_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:122_1_1_1_10_1_1"/>
( <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 1 or <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 2 or <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 3 )
 </span><b>by </b><i><a class="ref" href="scmfsa10.html#T45" target="_self">Th45</a>, <a class="ref" href="enumset1.html#D1">ENUMSET1:def 1</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="122_1_1_1_10_1_1_1"><b>suppose </b></a><a NAME="E1:122_1_1_1_10_1_1_1"/><i><font color="Green">E397</font></i>: 
<font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 1
 ;<br/><div class="add"><span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><font color="Maroon">b</font>,<font color="Maroon">f2</font>,<font color="Maroon">d3</font></span><a href="finseq_4.html#K3">*&gt;</a></span> <a href="funct_1.html#K1">.</a> 1 = 
<font color="Maroon">b</font>
<b>by </b><i><a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
<br/>.= 
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1
<b>by </b><i><a class="ref" href="scmfsa10.html#T31" target="_self">Th31</a>, <a class="ref" href="scmfsa10.html#T37" target="_self">Th37</a>, <a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
;<br/><b>hence </b><a NAME="E3:122_1_1_1_10_1_1_1"/>
<span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><font color="Maroon">b</font>,<font color="Maroon">f2</font>,<font color="Maroon">d3</font></span><a href="finseq_4.html#K3">*&gt;</a></span> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T46" target="_self">Th46</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="122_1_1_1_10_1_1_2"><b>suppose </b></a><a NAME="E1:122_1_1_1_10_1_1_2"/><i><font color="Green">E398</font></i>: 
<font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 2
 ;<br/><div class="add"><span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><font color="Maroon">b</font>,<font color="Maroon">f2</font>,<font color="Maroon">d3</font></span><a href="finseq_4.html#K3">*&gt;</a></span> <a href="funct_1.html#K1">.</a> 2 = 
<font color="Maroon">f2</font>
<b>by </b><i><a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
<br/>.= 
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 2
<b>by </b><i>, <a class="ref" href="scmfsa10.html#T40" target="_self">Th40</a>, <a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
;<br/><b>hence </b><a NAME="E3:122_1_1_1_10_1_1_2"/>
<span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><font color="Maroon">b</font>,<font color="Maroon">f2</font>,<font color="Maroon">d3</font></span><a href="finseq_4.html#K3">*&gt;</a></span> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T46" target="_self">Th46</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="122_1_1_1_10_1_1_3"><b>suppose </b></a><a NAME="E1:122_1_1_1_10_1_1_3"/><i><font color="Green">E399</font></i>: 
<font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 3
 ;<br/><div class="add"><span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><font color="Maroon">b</font>,<font color="Maroon">f2</font>,<font color="Maroon">d3</font></span><a href="finseq_4.html#K3">*&gt;</a></span> <a href="funct_1.html#K1">.</a> 3 = 
<font color="Maroon">d3</font>
<b>by </b><i><a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
<br/>.= 
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 3
<b>by </b><i><a class="ref" href="scmfsa10.html#T33" target="_self">Th33</a>, , <a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
;<br/><b>hence </b><a NAME="E3:122_1_1_1_10_1_1_3"/>
<span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><font color="Maroon">b</font>,<font color="Maroon">f2</font>,<font color="Maroon">d3</font></span><a href="finseq_4.html#K3">*&gt;</a></span> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T46" target="_self">Th46</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div><a NAME="E47:122_1_1_1_10"/><b>then </b><i><font color="Green">E400</font></i>: 
<span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><font color="Maroon">b</font>,<font color="Maroon">f2</font>,<font color="Maroon">d3</font></span><a href="finseq_4.html#K3">*&gt;</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T26" target="_self">Th26</a>, <a class="ref" href="scmfsa10.html#T28" target="_self">Th28</a>, <a class="ref" href="scmfsa10.html#T44" target="_self">Th44</a>, <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/><a NAME="E48:122_1_1_1_10"/>
(  <a href="ami_5.html#K1">InsCode</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="scmfsa_2.html#K16">:=</a> <font color="Maroon">f2</font>,<font color="Maroon">d3</font></span>)</span> <a href="hidden.html#R1">=</a> 9 &amp;  <a href="amistd_2.html#K4">AddressPart</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="scmfsa_2.html#K16">:=</a> <font color="Maroon">f2</font>,<font color="Maroon">d3</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><font color="Maroon">b</font>,<font color="Maroon">f2</font>,<font color="Maroon">d3</font></span><a href="finseq_4.html#K3">*&gt;</a></span> )
 <b>by </b><i>, <a class="ref" href="scmfsa_2.html#T50">SCMFSA_2:50</a></i>;<br/><b>hence </b><a NAME="E49:122_1_1_1_10"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T24" target="_self">Th24</a>, <a class="ref" href="scmfsa10.html#T25" target="_self">Th25</a>, <a class="ref" href="scmfsa10.html#T45" target="_self">Th45</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="122_1_1_1_11"><b>suppose </b></a><a NAME="E1:122_1_1_1_11"/><i><font color="Green">E401</font></i>: 
<font color="Maroon">T</font> <a href="hidden.html#R1">=</a> 10
 ;<br/><div class="add"><b>take </b>
 <a href="amistd_2.html#K1">PA</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span>
; <i><font color="Red">:: according to </font></i><a class="ref" href="amistd_2.html#D2">AMISTD_2:def 2</a><br/><b>thus </b><a NAME="E2:122_1_1_1_11"/>
 <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font> <a href="tarski.html#R1">c=</a>  <a href="card_3.html#K4">product</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="amistd_2.html#T9">AMISTD_2:9</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><br/><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/><b>assume </b><a NAME="E3:122_1_1_1_11"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="card_3.html#K4">product</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span>
 ;<br/><b>then consider </b><font color="Maroon">f</font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E5:122_1_1_1_11"/><i><font color="Green">E402</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font>
 <b>and </b><br/><a NAME="E6:122_1_1_1_11"/><i><font color="Green">E403</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span>
 <b>and </b><br/><a NAME="E7:122_1_1_1_11"/><i><font color="Green">E404</font></i>: 
for <font color="Olive">k</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">k</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span> holds <br/><font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font>
 <b>by </b><i><a class="ref" href="card_3.html#D5">CARD_3:def 5</a></i>;<br/><a NAME="E8:122_1_1_1_11"/><i><font color="Green">E405</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="enumset1.html#K1">{</a><span class="default">1,2,3</span><a href="enumset1.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T24" target="_self">Th24</a>, </i>;<br/><a NAME="E9:122_1_1_1_11"/><b>then </b><i><font color="Green">E406</font></i>: 
1 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="enumset1.html#D1">ENUMSET1:def 1</a></i>;<br/><a NAME="E10:122_1_1_1_11"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> 1
 <b>by </b><i><a class="ref" href="scmfsa10.html#T27" target="_self">Th27</a></i>;<br/><a NAME="E11:122_1_1_1_11"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R2">in</a>  <a href="card_3.html#K5">pi</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span>,1
 <b>by </b><i><a class="ref" href="scmfsa10.html#T29" target="_self">Th29</a>, <a class="ref" href="amistd_2.html#D1">AMISTD_2:def 1</a></i>;<br/><b>then consider </b><font color="Maroon">g</font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E13:122_1_1_1_11"/><i><font color="Green">E407</font></i>: 
<font color="Maroon">g</font> <a href="hidden.html#R2">in</a>  <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font>
 <b>and </b><br/><a NAME="E14:122_1_1_1_11"/><i><font color="Green">E408</font></i>: 
<font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1
 <b>by </b><i><a class="ref" href="card_3.html#D6">CARD_3:def 6</a></i>;<br/><a NAME="E15:122_1_1_1_11"/><i><font color="Green">E409</font></i>: 
2 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T28" target="_self">Th28</a>, <a class="ref" href="enumset1.html#D1">ENUMSET1:def 1</a></i>;<br/><a NAME="E16:122_1_1_1_11"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> 2
 <b>by </b><i><a class="ref" href="scmfsa10.html#T27" target="_self">Th27</a></i>;<br/><a NAME="E17:122_1_1_1_11"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R2">in</a>  <a href="card_3.html#K5">pi</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span>,2
 <b>by </b><i>, <a class="ref" href="amistd_2.html#D1">AMISTD_2:def 1</a></i>;<br/><b>then consider </b><font color="Maroon">h</font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E19:122_1_1_1_11"/><i><font color="Green">E410</font></i>: 
<font color="Maroon">h</font> <a href="hidden.html#R2">in</a>  <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font>
 <b>and </b><br/><a NAME="E20:122_1_1_1_11"/><i><font color="Green">E411</font></i>: 
<font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 2
 <b>by </b><i><a class="ref" href="card_3.html#D6">CARD_3:def 6</a></i>;<br/><a NAME="E21:122_1_1_1_11"/><i><font color="Green">E412</font></i>: 
3 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T28" target="_self">Th28</a>, <a class="ref" href="enumset1.html#D1">ENUMSET1:def 1</a></i>;<br/><a NAME="E22:122_1_1_1_11"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 3 <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> 3
 <b>by </b><i><a class="ref" href="scmfsa10.html#T27" target="_self">Th27</a></i>;<br/><a NAME="E23:122_1_1_1_11"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 3 <a href="hidden.html#R2">in</a>  <a href="card_3.html#K5">pi</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span>,3
 <b>by </b><i>, <a class="ref" href="amistd_2.html#D1">AMISTD_2:def 1</a></i>;<br/><b>then consider </b><font color="Maroon">z</font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E25:122_1_1_1_11"/><i><font color="Green">E413</font></i>: 
<font color="Maroon">z</font> <a href="hidden.html#R2">in</a>  <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font>
 <b>and </b><br/><a NAME="E26:122_1_1_1_11"/><i><font color="Green">E414</font></i>: 
<font color="Maroon">z</font> <a href="funct_1.html#K1">.</a> 3 <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 3
 <b>by </b><i><a class="ref" href="card_3.html#D6">CARD_3:def 6</a></i>;<br/><b>consider </b><font color="Maroon">I</font> being   <a href="ami_1.html#NM3">Instruction</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> <b> such that </b><br/><a NAME="E28:122_1_1_1_11"/><i><font color="Green">E415</font></i>: 
<font color="Maroon">g</font> <a href="hidden.html#R1">=</a>  <a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font>
 <b>and </b><br/><a NAME="E29:122_1_1_1_11"/><i><font color="Green">E416</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Maroon">T</font>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T30" target="_self">Th30</a></i>;<br/><b>consider </b><font color="Maroon">a</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">b</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">f1</font> being    <a href="scmfsa_2.html#M2">FinSeq-Location</a> <b> such that </b><br/><a NAME="E31:122_1_1_1_11"/><i><font color="Green">E417</font></i>: 
<font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f1</font>,<font color="Maroon">a</font> <a href="scmfsa_2.html#K17">:=</a> <font color="Maroon">b</font>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T24" target="_self">Th24</a>, <a class="ref" href="scmfsa10.html#T35" target="_self">Th35</a>, <a class="ref" href="scmfsa_2.html#T63">SCMFSA_2:63</a></i>;<br/><a NAME="E32:122_1_1_1_11"/><i><font color="Green">E418</font></i>: 
<font color="Maroon">g</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><font color="Maroon">b</font>,<font color="Maroon">f1</font>,<font color="Maroon">a</font></span><a href="finseq_4.html#K3">*&gt;</a></span>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T34" target="_self">Th34</a>, <a class="ref" href="scmfsa10.html#T36" target="_self">Th36</a>, </i>;<br/><b>consider </b><font color="Maroon">J</font> being   <a href="ami_1.html#NM3">Instruction</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> <b> such that </b><br/><a NAME="E34:122_1_1_1_11"/><i><font color="Green">E419</font></i>: 
<font color="Maroon">h</font> <a href="hidden.html#R1">=</a>  <a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">J</font>
 <b>and </b><br/><a NAME="E35:122_1_1_1_11"/><i><font color="Green">E420</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Maroon">T</font>
 <b>by </b><i/>;<br/><b>consider </b><font color="Maroon">d1</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">d2</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">f2</font> being    <a href="scmfsa_2.html#M2">FinSeq-Location</a> <b> such that </b><br/><a NAME="E37:122_1_1_1_11"/><i><font color="Green">E421</font></i>: 
<font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f2</font>,<font color="Maroon">d1</font> <a href="scmfsa_2.html#K17">:=</a> <font color="Maroon">d2</font>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T24" target="_self">Th24</a>, <a class="ref" href="scmfsa10.html#T39" target="_self">Th39</a>, <a class="ref" href="scmfsa_2.html#T63">SCMFSA_2:63</a></i>;<br/><a NAME="E38:122_1_1_1_11"/><i><font color="Green">E422</font></i>: 
<font color="Maroon">h</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><font color="Maroon">d2</font>,<font color="Maroon">f2</font>,<font color="Maroon">d1</font></span><a href="finseq_4.html#K3">*&gt;</a></span>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T38" target="_self">Th38</a>, , </i>;<br/><b>consider </b><font color="Maroon">K</font> being   <a href="ami_1.html#NM3">Instruction</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> <b> such that </b><br/><a NAME="E40:122_1_1_1_11"/><i><font color="Green">E423</font></i>: 
<font color="Maroon">z</font> <a href="hidden.html#R1">=</a>  <a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">K</font>
 <b>and </b><br/><a NAME="E41:122_1_1_1_11"/><i><font color="Green">E424</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">K</font> <a href="hidden.html#R1">=</a> <font color="Maroon">T</font>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T32" target="_self">Th32</a></i>;<br/><b>consider </b><font color="Maroon">d3</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">d4</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">f3</font> being    <a href="scmfsa_2.html#M2">FinSeq-Location</a> <b> such that </b><br/><a NAME="E43:122_1_1_1_11"/><i><font color="Green">E425</font></i>: 
<font color="Maroon">K</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f3</font>,<font color="Maroon">d3</font> <a href="scmfsa_2.html#K17">:=</a> <font color="Maroon">d4</font>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T24" target="_self">Th24</a>, <a class="ref" href="scmfsa10.html#T42" target="_self">Th42</a>, <a class="ref" href="scmfsa_2.html#T63">SCMFSA_2:63</a></i>;<br/><a NAME="E44:122_1_1_1_11"/><i><font color="Green">E426</font></i>: 
<font color="Maroon">z</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><font color="Maroon">d4</font>,<font color="Maroon">f3</font>,<font color="Maroon">d3</font></span><a href="finseq_4.html#K3">*&gt;</a></span>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T41" target="_self">Th41</a>, <a class="ref" href="scmfsa10.html#T43" target="_self">Th43</a>, </i>;<br/><a NAME="E45:122_1_1_1_11"/><i><font color="Green">E427</font></i>: 
 <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><font color="Maroon">b</font>,<font color="Maroon">f2</font>,<font color="Maroon">d3</font></span><a href="finseq_4.html#K3">*&gt;</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="enumset1.html#K1">{</a><span class="default">1,2,3</span><a href="enumset1.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="finseq_3.html#T1">FINSEQ_3:1</a>, <a class="ref" href="finseq_3.html#T30">FINSEQ_3:30</a></i>;<br/><a NAME="E46:122_1_1_1_11"/>
for <font color="Olive">k</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">k</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="enumset1.html#K1">{</a><span class="default">1,2,3</span><a href="enumset1.html#K1">}</a></span> holds <br/><span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><font color="Maroon">b</font>,<font color="Maroon">f2</font>,<font color="Maroon">d3</font></span><a href="finseq_4.html#K3">*&gt;</a></span> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="122_1_1_1_11_1"><b>proof </b></a><div class="add">

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

<b>assume </b><a NAME="E1:122_1_1_1_11_1"/><i><font color="Green">E428</font></i>: 
<font color="Maroon">k</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="enumset1.html#K1">{</a><span class="default">1,2,3</span><a href="enumset1.html#K1">}</a></span>
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="122_1_1_1_11_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:122_1_1_1_11_1_1"/>
( <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 1 or <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 2 or <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 3 )
 </span><b>by </b><i><a class="ref" href="scmfsa10.html#T45" target="_self">Th45</a>, <a class="ref" href="enumset1.html#D1">ENUMSET1:def 1</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="122_1_1_1_11_1_1_1"><b>suppose </b></a><a NAME="E1:122_1_1_1_11_1_1_1"/><i><font color="Green">E429</font></i>: 
<font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 1
 ;<br/><div class="add"><span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><font color="Maroon">b</font>,<font color="Maroon">f2</font>,<font color="Maroon">d3</font></span><a href="finseq_4.html#K3">*&gt;</a></span> <a href="funct_1.html#K1">.</a> 1 = 
<font color="Maroon">b</font>
<b>by </b><i><a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
<br/>.= 
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1
<b>by </b><i><a class="ref" href="scmfsa10.html#T31" target="_self">Th31</a>, <a class="ref" href="scmfsa10.html#T37" target="_self">Th37</a>, <a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
;<br/><b>hence </b><a NAME="E3:122_1_1_1_11_1_1_1"/>
<span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><font color="Maroon">b</font>,<font color="Maroon">f2</font>,<font color="Maroon">d3</font></span><a href="finseq_4.html#K3">*&gt;</a></span> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T46" target="_self">Th46</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="122_1_1_1_11_1_1_2"><b>suppose </b></a><a NAME="E1:122_1_1_1_11_1_1_2"/><i><font color="Green">E430</font></i>: 
<font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 2
 ;<br/><div class="add"><span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><font color="Maroon">b</font>,<font color="Maroon">f2</font>,<font color="Maroon">d3</font></span><a href="finseq_4.html#K3">*&gt;</a></span> <a href="funct_1.html#K1">.</a> 2 = 
<font color="Maroon">f2</font>
<b>by </b><i><a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
<br/>.= 
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 2
<b>by </b><i>, <a class="ref" href="scmfsa10.html#T40" target="_self">Th40</a>, <a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
;<br/><b>hence </b><a NAME="E3:122_1_1_1_11_1_1_2"/>
<span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><font color="Maroon">b</font>,<font color="Maroon">f2</font>,<font color="Maroon">d3</font></span><a href="finseq_4.html#K3">*&gt;</a></span> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T46" target="_self">Th46</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="122_1_1_1_11_1_1_3"><b>suppose </b></a><a NAME="E1:122_1_1_1_11_1_1_3"/><i><font color="Green">E431</font></i>: 
<font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 3
 ;<br/><div class="add"><span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><font color="Maroon">b</font>,<font color="Maroon">f2</font>,<font color="Maroon">d3</font></span><a href="finseq_4.html#K3">*&gt;</a></span> <a href="funct_1.html#K1">.</a> 3 = 
<font color="Maroon">d3</font>
<b>by </b><i><a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
<br/>.= 
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 3
<b>by </b><i><a class="ref" href="scmfsa10.html#T33" target="_self">Th33</a>, , <a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
;<br/><b>hence </b><a NAME="E3:122_1_1_1_11_1_1_3"/>
<span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><font color="Maroon">b</font>,<font color="Maroon">f2</font>,<font color="Maroon">d3</font></span><a href="finseq_4.html#K3">*&gt;</a></span> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T46" target="_self">Th46</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div><a NAME="E47:122_1_1_1_11"/><b>then </b><i><font color="Green">E432</font></i>: 
<span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><font color="Maroon">b</font>,<font color="Maroon">f2</font>,<font color="Maroon">d3</font></span><a href="finseq_4.html#K3">*&gt;</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T26" target="_self">Th26</a>, <a class="ref" href="scmfsa10.html#T28" target="_self">Th28</a>, <a class="ref" href="scmfsa10.html#T44" target="_self">Th44</a>, <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/><a NAME="E48:122_1_1_1_11"/>
(  <a href="ami_5.html#K1">InsCode</a> <span class="p1">(<span class="default"><font color="Maroon">f2</font>,<font color="Maroon">d3</font> <a href="scmfsa_2.html#K17">:=</a> <font color="Maroon">b</font></span>)</span> <a href="hidden.html#R1">=</a> 10 &amp;  <a href="amistd_2.html#K4">AddressPart</a> <span class="p1">(<span class="default"><font color="Maroon">f2</font>,<font color="Maroon">d3</font> <a href="scmfsa_2.html#K17">:=</a> <font color="Maroon">b</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><font color="Maroon">b</font>,<font color="Maroon">f2</font>,<font color="Maroon">d3</font></span><a href="finseq_4.html#K3">*&gt;</a></span> )
 <b>by </b><i>, <a class="ref" href="scmfsa_2.html#T51">SCMFSA_2:51</a></i>;<br/><b>hence </b><a NAME="E49:122_1_1_1_11"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T24" target="_self">Th24</a>, <a class="ref" href="scmfsa10.html#T25" target="_self">Th25</a>, <a class="ref" href="scmfsa10.html#T45" target="_self">Th45</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="122_1_1_1_12"><b>suppose </b></a><a NAME="E1:122_1_1_1_12"/><i><font color="Green">E433</font></i>: 
<font color="Maroon">T</font> <a href="hidden.html#R1">=</a> 11
 ;<br/><div class="add"><b>take </b>
 <a href="amistd_2.html#K1">PA</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span>
; <i><font color="Red">:: according to </font></i><a class="ref" href="amistd_2.html#D2">AMISTD_2:def 2</a><br/><b>thus </b><a NAME="E2:122_1_1_1_12"/>
 <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font> <a href="tarski.html#R1">c=</a>  <a href="card_3.html#K4">product</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="amistd_2.html#T9">AMISTD_2:9</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><br/><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/><b>assume </b><a NAME="E3:122_1_1_1_12"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="card_3.html#K4">product</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span>
 ;<br/><b>then consider </b><font color="Maroon">f</font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E5:122_1_1_1_12"/><i><font color="Green">E434</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font>
 <b>and </b><br/><a NAME="E6:122_1_1_1_12"/><i><font color="Green">E435</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span>
 <b>and </b><br/><a NAME="E7:122_1_1_1_12"/><i><font color="Green">E436</font></i>: 
for <font color="Olive">k</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">k</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span> holds <br/><font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font>
 <b>by </b><i><a class="ref" href="card_3.html#D5">CARD_3:def 5</a></i>;<br/><a NAME="E8:122_1_1_1_12"/><i><font color="Green">E437</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T24" target="_self">Th24</a>, </i>;<br/><a NAME="E9:122_1_1_1_12"/><b>then </b><i><font color="Green">E438</font></i>: 
1 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><a NAME="E10:122_1_1_1_12"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> 1
 <b>by </b><i><a class="ref" href="scmfsa10.html#T27" target="_self">Th27</a></i>;<br/><a NAME="E11:122_1_1_1_12"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R2">in</a>  <a href="card_3.html#K5">pi</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span>,1
 <b>by </b><i><a class="ref" href="scmfsa10.html#T29" target="_self">Th29</a>, <a class="ref" href="amistd_2.html#D1">AMISTD_2:def 1</a></i>;<br/><b>then consider </b><font color="Maroon">g</font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E13:122_1_1_1_12"/><i><font color="Green">E439</font></i>: 
<font color="Maroon">g</font> <a href="hidden.html#R2">in</a>  <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font>
 <b>and </b><br/><a NAME="E14:122_1_1_1_12"/><i><font color="Green">E440</font></i>: 
<font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1
 <b>by </b><i><a class="ref" href="card_3.html#D6">CARD_3:def 6</a></i>;<br/><a NAME="E15:122_1_1_1_12"/><i><font color="Green">E441</font></i>: 
2 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T28" target="_self">Th28</a>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><a NAME="E16:122_1_1_1_12"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> 2
 <b>by </b><i><a class="ref" href="scmfsa10.html#T27" target="_self">Th27</a></i>;<br/><a NAME="E17:122_1_1_1_12"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R2">in</a>  <a href="card_3.html#K5">pi</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span>,2
 <b>by </b><i>, <a class="ref" href="amistd_2.html#D1">AMISTD_2:def 1</a></i>;<br/><b>then consider </b><font color="Maroon">h</font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E19:122_1_1_1_12"/><i><font color="Green">E442</font></i>: 
<font color="Maroon">h</font> <a href="hidden.html#R2">in</a>  <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font>
 <b>and </b><br/><a NAME="E20:122_1_1_1_12"/><i><font color="Green">E443</font></i>: 
<font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 2
 <b>by </b><i><a class="ref" href="card_3.html#D6">CARD_3:def 6</a></i>;<br/><b>consider </b><font color="Maroon">I</font> being   <a href="ami_1.html#NM3">Instruction</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> <b> such that </b><br/><a NAME="E22:122_1_1_1_12"/><i><font color="Green">E444</font></i>: 
<font color="Maroon">g</font> <a href="hidden.html#R1">=</a>  <a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font>
 <b>and </b><br/><a NAME="E23:122_1_1_1_12"/><i><font color="Green">E445</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Maroon">T</font>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T30" target="_self">Th30</a></i>;<br/><b>consider </b><font color="Maroon">a</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">f1</font> being    <a href="scmfsa_2.html#M2">FinSeq-Location</a> <b> such that </b><br/><a NAME="E25:122_1_1_1_12"/><i><font color="Green">E446</font></i>: 
<font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="scmfsa_2.html#K18">:=len</a> <font color="Maroon">f1</font>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T24" target="_self">Th24</a>, <a class="ref" href="scmfsa10.html#T32" target="_self">Th32</a>, <a class="ref" href="scmfsa_2.html#T64">SCMFSA_2:64</a></i>;<br/><a NAME="E26:122_1_1_1_12"/><i><font color="Green">E447</font></i>: 
<font color="Maroon">g</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">f1</font></span><a href="finseq_4.html#K2">*&gt;</a></span>
 <b>by </b><i>, <a class="ref" href="scmfsa10.html#T33" target="_self">Th33</a>, </i>;<br/><b>consider </b><font color="Maroon">J</font> being   <a href="ami_1.html#NM3">Instruction</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> <b> such that </b><br/><a NAME="E28:122_1_1_1_12"/><i><font color="Green">E448</font></i>: 
<font color="Maroon">h</font> <a href="hidden.html#R1">=</a>  <a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">J</font>
 <b>and </b><br/><a NAME="E29:122_1_1_1_12"/><i><font color="Green">E449</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Maroon">T</font>
 <b>by </b><i/>;<br/><b>consider </b><font color="Maroon">b</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">f2</font> being    <a href="scmfsa_2.html#M2">FinSeq-Location</a> <b> such that </b><br/><a NAME="E31:122_1_1_1_12"/><i><font color="Green">E450</font></i>: 
<font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> <a href="scmfsa_2.html#K18">:=len</a> <font color="Maroon">f2</font>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T24" target="_self">Th24</a>, <a class="ref" href="scmfsa10.html#T36" target="_self">Th36</a>, <a class="ref" href="scmfsa_2.html#T64">SCMFSA_2:64</a></i>;<br/><a NAME="E32:122_1_1_1_12"/><i><font color="Green">E451</font></i>: 
<font color="Maroon">h</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">b</font>,<font color="Maroon">f2</font></span><a href="finseq_4.html#K2">*&gt;</a></span>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T35" target="_self">Th35</a>, <a class="ref" href="scmfsa10.html#T37" target="_self">Th37</a>, </i>;<br/><a NAME="E33:122_1_1_1_12"/><i><font color="Green">E452</font></i>: 
 <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">f2</font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span>
 <b>by </b><i><a class="ref" href="finseq_1.html#T4">FINSEQ_1:4</a>, <a class="ref" href="finseq_3.html#T29">FINSEQ_3:29</a></i>;<br/><a NAME="E34:122_1_1_1_12"/>
for <font color="Olive">k</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">k</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span> holds <br/><span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">f2</font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="122_1_1_1_12_1"><b>proof </b></a><div class="add">

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

<b>assume </b><a NAME="E1:122_1_1_1_12_1"/><i><font color="Green">E453</font></i>: 
<font color="Maroon">k</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span>
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="122_1_1_1_12_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:122_1_1_1_12_1_1"/>
( <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 1 or <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 2 )
 </span><b>by </b><i>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="122_1_1_1_12_1_1_1"><b>suppose </b></a><a NAME="E1:122_1_1_1_12_1_1_1"/><i><font color="Green">E454</font></i>: 
<font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 1
 ;<br/><div class="add"><span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">f2</font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="funct_1.html#K1">.</a> 1 = 
<font color="Maroon">a</font>
<b>by </b><i><a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>
<br/>.= 
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1
<b>by </b><i><a class="ref" href="scmfsa10.html#T31" target="_self">Th31</a>, <a class="ref" href="scmfsa10.html#T34" target="_self">Th34</a>, <a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>
;<br/><b>hence </b><a NAME="E3:122_1_1_1_12_1_1_1"/>
<span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">f2</font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T40" target="_self">Th40</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="122_1_1_1_12_1_1_2"><b>suppose </b></a><a NAME="E1:122_1_1_1_12_1_1_2"/><i><font color="Green">E455</font></i>: 
<font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 2
 ;<br/><div class="add"><span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">f2</font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="funct_1.html#K1">.</a> 2 = 
<font color="Maroon">f2</font>
<b>by </b><i><a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>
<br/>.= 
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 2
<b>by </b><i>, <a class="ref" href="scmfsa10.html#T38" target="_self">Th38</a>, <a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>
;<br/><b>hence </b><a NAME="E3:122_1_1_1_12_1_1_2"/>
<span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">f2</font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T40" target="_self">Th40</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div><a NAME="E35:122_1_1_1_12"/><b>then </b><i><font color="Green">E456</font></i>: 
<span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">f2</font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T26" target="_self">Th26</a>, <a class="ref" href="scmfsa10.html#T28" target="_self">Th28</a>, <a class="ref" href="scmfsa10.html#T39" target="_self">Th39</a>, <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/><a NAME="E36:122_1_1_1_12"/>
(  <a href="ami_5.html#K1">InsCode</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="scmfsa_2.html#K18">:=len</a> <font color="Maroon">f2</font></span>)</span> <a href="hidden.html#R1">=</a> 11 &amp;  <a href="amistd_2.html#K4">AddressPart</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="scmfsa_2.html#K18">:=len</a> <font color="Maroon">f2</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">f2</font></span><a href="finseq_4.html#K2">*&gt;</a></span> )
 <b>by </b><i>, <a class="ref" href="scmfsa_2.html#T52">SCMFSA_2:52</a></i>;<br/><b>hence </b><a NAME="E37:122_1_1_1_12"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T24" target="_self">Th24</a>, <a class="ref" href="scmfsa10.html#T25" target="_self">Th25</a>, </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="122_1_1_1_13"><b>suppose </b></a><a NAME="E1:122_1_1_1_13"/><i><font color="Green">E457</font></i>: 
<font color="Maroon">T</font> <a href="hidden.html#R1">=</a> 12
 ;<br/><div class="add"><b>take </b>
 <a href="amistd_2.html#K1">PA</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span>
; <i><font color="Red">:: according to </font></i><a class="ref" href="amistd_2.html#D2">AMISTD_2:def 2</a><br/><b>thus </b><a NAME="E2:122_1_1_1_13"/>
 <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font> <a href="tarski.html#R1">c=</a>  <a href="card_3.html#K4">product</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="amistd_2.html#T9">AMISTD_2:9</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><br/><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/><b>assume </b><a NAME="E3:122_1_1_1_13"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="card_3.html#K4">product</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span>
 ;<br/><b>then consider </b><font color="Maroon">f</font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E5:122_1_1_1_13"/><i><font color="Green">E458</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font>
 <b>and </b><br/><a NAME="E6:122_1_1_1_13"/><i><font color="Green">E459</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span>
 <b>and </b><br/><a NAME="E7:122_1_1_1_13"/><i><font color="Green">E460</font></i>: 
for <font color="Olive">k</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">k</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span> holds <br/><font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font>
 <b>by </b><i><a class="ref" href="card_3.html#D5">CARD_3:def 5</a></i>;<br/><a NAME="E8:122_1_1_1_13"/><i><font color="Green">E461</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T24" target="_self">Th24</a>, </i>;<br/><a NAME="E9:122_1_1_1_13"/><b>then </b><i><font color="Green">E462</font></i>: 
1 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><a NAME="E10:122_1_1_1_13"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> 1
 <b>by </b><i><a class="ref" href="scmfsa10.html#T27" target="_self">Th27</a></i>;<br/><a NAME="E11:122_1_1_1_13"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R2">in</a>  <a href="card_3.html#K5">pi</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span>,1
 <b>by </b><i><a class="ref" href="scmfsa10.html#T29" target="_self">Th29</a>, <a class="ref" href="amistd_2.html#D1">AMISTD_2:def 1</a></i>;<br/><b>then consider </b><font color="Maroon">g</font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E13:122_1_1_1_13"/><i><font color="Green">E463</font></i>: 
<font color="Maroon">g</font> <a href="hidden.html#R2">in</a>  <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font>
 <b>and </b><br/><a NAME="E14:122_1_1_1_13"/><i><font color="Green">E464</font></i>: 
<font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1
 <b>by </b><i><a class="ref" href="card_3.html#D6">CARD_3:def 6</a></i>;<br/><a NAME="E15:122_1_1_1_13"/><i><font color="Green">E465</font></i>: 
2 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T28" target="_self">Th28</a>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><a NAME="E16:122_1_1_1_13"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> 2
 <b>by </b><i><a class="ref" href="scmfsa10.html#T27" target="_self">Th27</a></i>;<br/><a NAME="E17:122_1_1_1_13"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R2">in</a>  <a href="card_3.html#K5">pi</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font></span>)</span>,2
 <b>by </b><i>, <a class="ref" href="amistd_2.html#D1">AMISTD_2:def 1</a></i>;<br/><b>then consider </b><font color="Maroon">h</font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E19:122_1_1_1_13"/><i><font color="Green">E466</font></i>: 
<font color="Maroon">h</font> <a href="hidden.html#R2">in</a>  <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font>
 <b>and </b><br/><a NAME="E20:122_1_1_1_13"/><i><font color="Green">E467</font></i>: 
<font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 2
 <b>by </b><i><a class="ref" href="card_3.html#D6">CARD_3:def 6</a></i>;<br/><b>consider </b><font color="Maroon">I</font> being   <a href="ami_1.html#NM3">Instruction</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> <b> such that </b><br/><a NAME="E22:122_1_1_1_13"/><i><font color="Green">E468</font></i>: 
<font color="Maroon">g</font> <a href="hidden.html#R1">=</a>  <a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font>
 <b>and </b><br/><a NAME="E23:122_1_1_1_13"/><i><font color="Green">E469</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Maroon">T</font>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T30" target="_self">Th30</a></i>;<br/><b>consider </b><font color="Maroon">a</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">f1</font> being    <a href="scmfsa_2.html#M2">FinSeq-Location</a> <b> such that </b><br/><a NAME="E25:122_1_1_1_13"/><i><font color="Green">E470</font></i>: 
<font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f1</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">a</font>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T24" target="_self">Th24</a>, <a class="ref" href="scmfsa10.html#T32" target="_self">Th32</a>, <a class="ref" href="scmfsa_2.html#T65">SCMFSA_2:65</a></i>;<br/><a NAME="E26:122_1_1_1_13"/><i><font color="Green">E471</font></i>: 
<font color="Maroon">g</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">f1</font></span><a href="finseq_4.html#K2">*&gt;</a></span>
 <b>by </b><i>, <a class="ref" href="scmfsa10.html#T33" target="_self">Th33</a>, </i>;<br/><b>consider </b><font color="Maroon">J</font> being   <a href="ami_1.html#NM3">Instruction</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> <b> such that </b><br/><a NAME="E28:122_1_1_1_13"/><i><font color="Green">E472</font></i>: 
<font color="Maroon">h</font> <a href="hidden.html#R1">=</a>  <a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">J</font>
 <b>and </b><br/><a NAME="E29:122_1_1_1_13"/><i><font color="Green">E473</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Maroon">T</font>
 <b>by </b><i/>;<br/><b>consider </b><font color="Maroon">b</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">f2</font> being    <a href="scmfsa_2.html#M2">FinSeq-Location</a> <b> such that </b><br/><a NAME="E31:122_1_1_1_13"/><i><font color="Green">E474</font></i>: 
<font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f2</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">b</font>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T24" target="_self">Th24</a>, <a class="ref" href="scmfsa10.html#T36" target="_self">Th36</a>, <a class="ref" href="scmfsa_2.html#T65">SCMFSA_2:65</a></i>;<br/><a NAME="E32:122_1_1_1_13"/><i><font color="Green">E475</font></i>: 
<font color="Maroon">h</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">b</font>,<font color="Maroon">f2</font></span><a href="finseq_4.html#K2">*&gt;</a></span>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T35" target="_self">Th35</a>, <a class="ref" href="scmfsa10.html#T37" target="_self">Th37</a>, </i>;<br/><a NAME="E33:122_1_1_1_13"/><i><font color="Green">E476</font></i>: 
 <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">f2</font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span>
 <b>by </b><i><a class="ref" href="finseq_1.html#T4">FINSEQ_1:4</a>, <a class="ref" href="finseq_3.html#T29">FINSEQ_3:29</a></i>;<br/><a NAME="E34:122_1_1_1_13"/>
for <font color="Olive">k</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">k</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span> holds <br/><span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">f2</font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="122_1_1_1_13_1"><b>proof </b></a><div class="add">

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

<b>assume </b><a NAME="E1:122_1_1_1_13_1"/><i><font color="Green">E477</font></i>: 
<font color="Maroon">k</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span>
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="122_1_1_1_13_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:122_1_1_1_13_1_1"/>
( <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 1 or <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 2 )
 </span><b>by </b><i>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="122_1_1_1_13_1_1_1"><b>suppose </b></a><a NAME="E1:122_1_1_1_13_1_1_1"/><i><font color="Green">E478</font></i>: 
<font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 1
 ;<br/><div class="add"><span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">f2</font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="funct_1.html#K1">.</a> 1 = 
<font color="Maroon">a</font>
<b>by </b><i><a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>
<br/>.= 
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1
<b>by </b><i><a class="ref" href="scmfsa10.html#T31" target="_self">Th31</a>, <a class="ref" href="scmfsa10.html#T34" target="_self">Th34</a>, <a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>
;<br/><b>hence </b><a NAME="E3:122_1_1_1_13_1_1_1"/>
<span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">f2</font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T40" target="_self">Th40</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="122_1_1_1_13_1_1_2"><b>suppose </b></a><a NAME="E1:122_1_1_1_13_1_1_2"/><i><font color="Green">E479</font></i>: 
<font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 2
 ;<br/><div class="add"><span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">f2</font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="funct_1.html#K1">.</a> 2 = 
<font color="Maroon">f2</font>
<b>by </b><i><a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>
<br/>.= 
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 2
<b>by </b><i>, <a class="ref" href="scmfsa10.html#T38" target="_self">Th38</a>, <a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>
;<br/><b>hence </b><a NAME="E3:122_1_1_1_13_1_1_2"/>
<span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">f2</font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T40" target="_self">Th40</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div><a NAME="E35:122_1_1_1_13"/><b>then </b><i><font color="Green">E480</font></i>: 
<span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">f2</font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T26" target="_self">Th26</a>, <a class="ref" href="scmfsa10.html#T28" target="_self">Th28</a>, <a class="ref" href="scmfsa10.html#T39" target="_self">Th39</a>, <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/><a NAME="E36:122_1_1_1_13"/>
(  <a href="ami_5.html#K1">InsCode</a> <span class="p1">(<span class="default"><font color="Maroon">f2</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">a</font></span>)</span> <a href="hidden.html#R1">=</a> 12 &amp;  <a href="amistd_2.html#K4">AddressPart</a> <span class="p1">(<span class="default"><font color="Maroon">f2</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">a</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">f2</font></span><a href="finseq_4.html#K2">*&gt;</a></span> )
 <b>by </b><i>, <a class="ref" href="scmfsa_2.html#T53">SCMFSA_2:53</a></i>;<br/><b>hence </b><a NAME="E37:122_1_1_1_13"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T24" target="_self">Th24</a>, <a class="ref" href="scmfsa10.html#T25" target="_self">Th25</a>, </i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div>
