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<b>let </b><font color="Maroon">T</font> be   <a href="ami_1.html#NM8">InsType</a> of <a href="ami_3.html#K1">SCM</a> ;<br/>

<b>assume </b><a NAME="E1:18"/><i><font color="Green">E42</font></i>: 
<font color="Maroon">T</font> <a href="hidden.html#R1">=</a> 7
 ;<br/>

<b>consider </b><font color="Maroon">i1</font> being   <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="ami_3.html#K1">SCM</a> , <font color="Maroon">a</font> being    <a href="ami_3.html#M1">Data-Location</a> ;<br/>
<a NAME="E3:18"/><i><font color="Green">E47</font></i>: 
 <a href="amistd_2.html#K4">AddressPart</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="ami_3.html#K9">=0_goto</a> <font color="Maroon">i1</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">i1</font>,<font color="Maroon">a</font></span><a href="finseq_1.html#K10">*&gt;</a></span>
 
<b>by </b><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">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:18_1"/><i><font color="Green">E49</font></i>: 
<font color="Maroon">x</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>
 ;<br/><a NAME="E2:18_1"/>
 <a href="ami_5.html#K1">InsCode</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="ami_3.html#K9">=0_goto</a> <font color="Maroon">i1</font></span>)</span> <a href="hidden.html#R1">=</a> 7
 <b>by </b><i><a class="ref" href="mcart_1.html#T7">MCART_1:7</a></i>;<br/><a NAME="E3:18_1"/><b>then </b>
 <a href="amistd_2.html#K4">AddressPart</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="ami_3.html#K9">=0_goto</a> <font color="Maroon">i1</font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font>
 <b>by </b><i/>;<br/><a NAME="E4:18_1"/><b>then </b>
<font color="Maroon">x</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"><font color="Maroon">a</font> <a href="ami_3.html#K9">=0_goto</a> <font color="Maroon">i1</font></span>)</span></span>)</span>
 <b>by </b><i>, <a class="ref" href="amistd_2.html#D1">AMISTD_2:def 1</a></i>;<br/><b>hence </b><a NAME="E5:18_1"/>
<font color="Maroon">x</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="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">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="E5:18"/><i><font color="Green">E52</font></i>: 
<font color="Maroon">x</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="E6:18"/>
for <font color="Olive">f</font> being  <a href="funct_1.html#NM1">Function</a>  st <font color="Olive">f</font> <a href="hidden.html#R2">in</a>  <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font> holds <br/><font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Olive">f</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="18_2"><b>proof </b></a><div class="add">

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

<b>assume </b><a NAME="E1:18_2"/>
<font color="Maroon">f</font> <a href="hidden.html#R2">in</a>  <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">T</font>
 ;<br/>

<b>then consider </b><font color="Maroon">I</font> being   <a href="ami_1.html#NM3">Instruction</a> of <a href="ami_3.html#K1">SCM</a> <b> such that </b><br/><a NAME="E3:18_2"/><i><font color="Green">E53</font></i>: 
<font color="Maroon">f</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="E4:18_2"/><i><font color="Green">E54</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>
 ;<br/>
<b>consider </b><font color="Maroon">i1</font> being   <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="ami_3.html#K1">SCM</a> , <font color="Maroon">a</font> being    <a href="ami_3.html#M1">Data-Location</a> <b> such that </b><br/><a NAME="E6:18_2"/><i><font color="Green">E79</font></i>: 
<font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="ami_3.html#K9">=0_goto</a> <font color="Maroon">i1</font>
 <b>by </b><i>, , <a class="ref" href="ami_5.html#T53">AMI_5:53</a></i>;<br/>
<a NAME="E7:18_2"/>
<font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">i1</font>,<font color="Maroon">a</font></span><a href="finseq_1.html#K10">*&gt;</a></span>
 
<b>by </b><i>, , </i>;<br/>
<b>hence </b><a NAME="E8:18_2"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font>
 <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/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E7:18"/>
<font color="Maroon">x</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>
 <b>by </b><i><a class="ref" href="amistd_2.html#D1">AMISTD_2:def 1</a></i>;<br/>


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