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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="ami_1.html#NM8">InsType</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> ;<br/>

<b>assume </b><a NAME="E1:39"/><i><font color="Green">E39</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> 5
 ;<br/>

<b>consider </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> being    <a href="scmfsa_2.html#M1">Int-Location</a> ;<br/>
<a NAME="E3:39"/><i><font color="Green">E40</font></i>: 
 <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">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></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">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span>
 
<b>by </b><i><a class="ref" href="scmfsa10.html#T22" target="_self">Th22</a></i>;<br/>
<div><b>hereby </b> <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a>,<a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a>
<div class="add"><b>let </b><font color="Maroon">c<sub>4</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:39_1"/><i><font color="Green">E41</font></i>: 
<font color="Maroon">c<sub>4</sub></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">c<sub>1</sub></font></span>)</span></span>)</span>
 ;<br/><a NAME="E2:39_1"/>
 <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">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a> 5
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T46">SCMFSA_2:46</a></i>;<br/><a NAME="E3:39_1"/><b>then </b>
 <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">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E1:39"><i><font color="Green">E39</font></i></a></i>;<br/><a NAME="E4:39_1"/><b>then </b>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K12">Divide</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E1:39_1"><i><font color="Green">E41</font></i></a>, <a class="ref" href="amistd_2.html#D1">AMISTD_2:def 1</a></i>;<br/><b>hence </b><a NAME="E5:39_1"/>
<font color="Maroon">c<sub>4</sub></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>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E3:39"><i><font color="Green">E40</font></i></a>, <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/></div>
<b>end;</b></div>

<b>let </b><font color="Maroon">c<sub>4</sub></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="E5:39"/><i><font color="Green">E41</font></i>: 
<font color="Maroon">c<sub>4</sub></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/>

<a NAME="E6:39"/>
for <font color="Olive">b<sub>1</sub></font> being  <a href="funct_1.html#NM1">Function</a> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font> holds <br/><font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Olive">b<sub>1</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="39_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>5</sub></font> be   <a href="funct_1.html#NM1">Function</a>;<br/>

<b>assume </b><a NAME="E1:39_2"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>6</sub></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="E3:39_2"/><i><font color="Green">E42</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">c<sub>6</sub></font>
 <b>and </b><br/><a NAME="E4:39_2"/><i><font color="Green">E43</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>
<b>consider </b><font color="Maroon">c<sub>7</sub></font>, <font color="Maroon">c<sub>8</sub></font> being    <a href="scmfsa_2.html#M1">Int-Location</a> <b> such that </b><br/><a NAME="E6:39_2"/><i><font color="Green">E44</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K12">Divide</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E1:39"><i><font color="Green">E39</font></i></a>, <a class="txt" href="scmfsa10.html#E4:39_2"><i><font color="Green">E43</font></i></a>, <a class="ref" href="scmfsa_2.html#T58">SCMFSA_2:58</a></i>;<br/>
<a NAME="E7:39_2"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span>
 
<b>by </b><i><a class="txt" href="scmfsa10.html#E3:39_2"><i><font color="Green">E42</font></i></a>, <a class="txt" href="scmfsa10.html#E6:39_2"><i><font color="Green">E44</font></i></a>, <a class="ref" href="scmfsa10.html#T22" target="_self">Th22</a></i>;<br/>
<b>hence </b><a NAME="E8:39_2"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E5:39"><i><font color="Green">E41</font></i></a>, <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/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E7:39"/>
<font color="Maroon">c<sub>4</sub></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">c<sub>1</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="amistd_2.html#D1">AMISTD_2:def 1</a></i>;<br/>


</div>
