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<b>let </b><font color="Maroon">N</font> be  <a href="setfam_1.html#V1">with_non-empty_elements</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">S</font> be  non <a href="struct_0.html#V3">empty</a> non <a href="ami_1.html#V2">void</a> <a href="amistd_2.html#V2" target="_self">homogeneous</a>  <a href="ami_1.html#L1">AMI-Struct</a> of <font color="Maroon">N</font>;<br/><b>let </b><font color="Maroon">I</font> be   <a href="ami_1.html#NM3">Instruction</a> of <font color="Maroon">S</font>;<br/><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/>







<b>assume </b><a NAME="E1:48"/><i><font color="Green">E44</font></i>: 
<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" target="_self">AddressPart</a> <font color="Maroon">I</font></span>)</span>
 ;<br/>

<a NAME="E2:48"/><i><font color="Green">E45</font></i>: 
 <a href="amistd_2.html#K4" target="_self">AddressPart</a> <font color="Maroon">I</font> <a href="hidden.html#R2">in</a>  <a href="amistd_2.html#K5" target="_self">AddressParts</a> <span class="p1">(<span class="default"><a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font></span>)</span>
 
;<br/>
<b>assume </b><a NAME="E3:48"/><i><font color="Green">E56</font></i>: 
<span class="p1">(<span class="default"><a href="amistd_2.html#K1" target="_self">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5" target="_self">AddressParts</a> <span class="p3">(<span class="default"><a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <font color="Maroon">S</font>
 ;<br/>

<a NAME="E4:48"/>
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" target="_self">AddressParts</a> <span class="p1">(<span class="default"><a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font></span>)</span> 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="48_1"><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="E1:48_1"/>
<font color="Maroon">f</font> <a href="hidden.html#R2">in</a>  <a href="amistd_2.html#K5" target="_self">AddressParts</a> <span class="p1">(<span class="default"><a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font></span>)</span>
 ;<br/>

<a NAME="E2:48_1"/><b>then </b>
 ex <font color="Olive">J</font> being  <a href="ami_1.html#NM3">Instruction</a> of <font color="Maroon">S</font> st <br/>( <font color="Maroon">f</font> <a href="hidden.html#R1">=</a>  <a href="amistd_2.html#K4" target="_self">AddressPart</a> <font color="Olive">J</font> &amp;  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="ami_5.html#K1">InsCode</a> <font color="Olive">J</font> )
 
;<br/>
<b>hence </b><a NAME="E3:48_1"/>
<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>, </i>;<br/>


</div><b>end;</b></div>
<a NAME="E5:48"/><b>then </b>
<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" target="_self">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5" target="_self">AddressParts</a> <span class="p3">(<span class="default"><a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E6:48"/><b>then </b>
<span class="p1">(<span class="default"><a href="amistd_2.html#K1" target="_self">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5" target="_self">AddressParts</a> <span class="p3">(<span class="default"><a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="card_3.html#K5">pi</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K5" target="_self">AddressParts</a> <span class="p2">(<span class="default"><a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font></span>)</span></span>)</span>,<font color="Maroon">x</font>
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E7:48"/>
<span class="p1">(<span class="default"><a href="amistd_2.html#K4" target="_self">AddressPart</a> <font color="Maroon">I</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> is   <a href="ami_1.html#NM2">Instruction-Location</a> of <font color="Maroon">S</font>
 <b>by </b><i>, , <a class="ref" href="card_3.html#D6">CARD_3:def 6</a></i>;<br/>


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