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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="ami_1.html#V5">IC-Ins-separated</a> <a href="ami_1.html#V8">definite</a> <a href="amistd_1.html#V4">standard</a>  <a href="ami_1.html#L1">AMI-Struct</a> of <font color="Maroon">N</font>;<br/><b>let </b><font color="Maroon">F</font> be  non <a href="xboole_0.html#V1">empty</a> <a href="ami_3.html#V1">programmed</a>  <a href="ami_1.html#M1">FinPartState</a> of <font color="Maroon">S</font>, <font color="Maroon">G</font> be  non <a href="xboole_0.html#V1">empty</a> <a href="ami_3.html#V1">programmed</a>  <a href="ami_1.html#M1">FinPartState</a> of <font color="Maroon">S</font>;<br/>





<b>assume </b><a NAME="E1:38"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">F</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">G</font>
 ;<br/>

<b>consider </b><font color="Maroon">M</font> being  non <a href="xboole_0.html#V1">empty</a> <a href="subset_1.html#NM2">Subset</a> of <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E3:38"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">M</font> <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="amistd_1.html#K7">locnum</a> <font color="Olive">l</font></span>)</span> where <font color="Olive">l</font> is    <a href="subset_1.html#M1">Element</a> of the <a href="ami_1.html#U2">Instruction-Locations</a> of <font color="Maroon">S</font> : <font color="Olive">l</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">F</font> </span>}</span> 
 <b>and </b><br/><a NAME="E4:38"/><i><font color="Green">E38</font></i>: 
 <a href="amistd_3.html#K2" target="_self">FirstLoc</a> <font color="Maroon">F</font> <a href="hidden.html#R1">=</a>  <a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<span class="p1">(<span class="default"><a href="cqc_sim1.html#K10">min</a> <font color="Maroon">M</font></span>)</span>
 <b>by </b><i/>;<br/>
<b>consider </b><font color="Maroon">N</font> being  non <a href="xboole_0.html#V1">empty</a> <a href="subset_1.html#NM2">Subset</a> of <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E6:38"/><i><font color="Green">E40</font></i>: 
<font color="Maroon">N</font> <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="amistd_1.html#K7">locnum</a> <font color="Olive">l</font></span>)</span> where <font color="Olive">l</font> is    <a href="subset_1.html#M1">Element</a> of the <a href="ami_1.html#U2">Instruction-Locations</a> of <font color="Maroon">S</font> : <font color="Olive">l</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">G</font> </span>}</span> 
 <b>and </b><br/><a NAME="E7:38"/><i><font color="Green">E42</font></i>: 
 <a href="amistd_3.html#K2" target="_self">FirstLoc</a> <font color="Maroon">G</font> <a href="hidden.html#R1">=</a>  <a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<span class="p1">(<span class="default"><a href="cqc_sim1.html#K10">min</a> <font color="Maroon">N</font></span>)</span>
 <b>by </b><i/>;<br/>
<a NAME="E8:38"/>
<font color="Maroon">M</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">N</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="38_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">a</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="E1:38_1"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">M</font>
 ;<br/>

<a NAME="E2:38_1"/><b>then </b><i><font color="Green">E59</font></i>: 
 ex <font color="Olive">l</font> being   <a href="subset_1.html#M1">Element</a> of the <a href="ami_1.html#U2">Instruction-Locations</a> of <font color="Maroon">S</font> st <br/>( <font color="Maroon">a</font> <a href="hidden.html#R1">=</a>  <a href="amistd_1.html#K7">locnum</a> <font color="Olive">l</font> &amp; <font color="Olive">l</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/>;<br/>
<a NAME="E3:38_1"/>
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">F</font> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">G</font>
 
<b>by </b><i>, <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>;<br/>
<b>hence </b><a NAME="E4:38_1"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">N</font>
 <b>by </b><i>, </i>;<br/>


</div><b>end;</b></div>
<a NAME="E9:38"/><b>then </b>
 <a href="cqc_sim1.html#K10">min</a> <font color="Maroon">N</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="cqc_sim1.html#K10">min</a> <font color="Maroon">M</font>
 
<b>by </b><i><a class="ref" href="cqc_sim1.html#T19">CQC_SIM1:19</a></i>;<br/>
<b>hence </b><a NAME="E10:38"/>
 <a href="amistd_3.html#K2" target="_self">FirstLoc</a> <font color="Maroon">G</font> <a href="amistd_1.html#R1">&lt;=</a>  <a href="amistd_3.html#K2" target="_self">FirstLoc</a> <font color="Maroon">F</font>
 <b>by </b><i>, , <a class="ref" href="amistd_1.html#T28">AMISTD_1:28</a></i>;<br/>


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