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

<b>let </b><font color="Maroon" title="c1">N</font> be  <a href="setfam_1.html#V1" title="SETFAM_1:attr.1">with_non-empty_elements</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c2">S</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a> non <a href="ami_1.html#V2" title="AMI_1:attr.2">void</a> <a href="ami_1.html#V5" title="AMI_1:attr.5">IC-Ins-separated</a> <a href="ami_1.html#V8" title="AMI_1:attr.8">definite</a> <a href="amistd_1.html#V4" title="AMISTD_1:attr.4">standard</a>  <a href="ami_1.html#L1" title="AMI_1:struct.1">AMI-Struct</a> of <font color="Maroon" title="c1">N</font>;<br/><b>let </b><font color="Maroon" title="c3">F</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="ami_3.html#V1" title="AMI_3:attr.1">programmed</a> <a href="amistd_1.html#V9" title="AMISTD_1:attr.9">lower</a>  <a href="ami_1.html#M1" title="AMI_1:mode.1">FinPartState</a> of <font color="Maroon" title="c2">S</font>;<br/>





<b>consider </b><font color="Maroon" title="c4">M</font> being  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <b> such that </b><br/><a NAME="E2:40"/>
<font color="Maroon" title="c4">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="amistd_1.html#K7" title="AMISTD_1:func.7">locnum</a> <font color="Olive" title="b1">l</font></span>)</span> where <font color="Olive" title="b1">l</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instruction-Locations</a> of <font color="Maroon" title="c2">S</font> : <font color="Olive" title="b1">l</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c3">F</font> </span>}</span> 
 <b>and </b><br/><a NAME="E3:40"/><i><font color="Green" title="E21">A1</font></i>: 
 <a href="amistd_3.html#K2" title="AMISTD_3:func.2">FirstLoc</a> <font color="Maroon" title="c3">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<span class="p1">(<span class="default"><a href="cqc_sim1.html#K10" title="CQC_SIM1:func.10">min</a> <font color="Maroon" title="c4">M</font></span>)</span>
 <b>by </b><i><a class="ref" href="amistd_3.html#D2" target="_self" title="AMISTD_3:def.2">Def2</a></i>;<br/>
<a NAME="E4:40"/><i><font color="Green" title="E22">A2</font></i>: 
 <a href="amistd_3.html#K2" title="AMISTD_3:func.2">FirstLoc</a> <font color="Maroon" title="c3">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c3">F</font>
 
<b>by </b><i><a class="ref" href="amistd_3.html#T21" target="_self" title="AMISTD_3:th.21">Th21</a></i>;<br/>
<a NAME="E5:40"/><i><font color="Green" title="E23">A3</font></i>: 
 <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,0 <a href="amistd_1.html#R1" title="AMISTD_1:pred.1">&lt;=</a>  <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<span class="p1">(<span class="default"><a href="cqc_sim1.html#K10" title="CQC_SIM1:func.10">min</a> <font color="Maroon" title="c4">M</font></span>)</span>
 
<b>by </b><i><a class="ref" href="amistd_1.html#T28" title="AMISTD_1:th.28">AMISTD_1:28</a></i>;<br/>
<a NAME="E6:40"/><b>then </b>
 <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,0 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c3">F</font>
 
<b>by </b><i><a class="txt" href="amistd_3.html#E3:40"><i><font color="Green" title="E21">A1</font></i></a>, <a class="txt" href="amistd_3.html#E4:40"><i><font color="Green" title="E22">A2</font></i></a>, <a class="ref" href="amistd_1.html#D20" title="AMISTD_1:def.20">AMISTD_1:def 20</a></i>;<br/>
<a NAME="E7:40"/><b>then </b>
 <a href="amistd_3.html#K2" title="AMISTD_3:func.2">FirstLoc</a> <font color="Maroon" title="c3">F</font> <a href="amistd_1.html#R1" title="AMISTD_1:pred.1">&lt;=</a>  <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,0
 
<b>by </b><i><a class="ref" href="amistd_3.html#T23" target="_self" title="AMISTD_3:th.23">Th23</a></i>;<br/>
<b>hence </b><a NAME="E8:40"/>
 <a href="amistd_3.html#K2" title="AMISTD_3:func.2">FirstLoc</a> <font color="Maroon" title="c3">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,0
 <b>by </b><i><a class="txt" href="amistd_3.html#E3:40"><i><font color="Green" title="E21">A1</font></i></a>, <a class="txt" href="amistd_3.html#E5:40"><i><font color="Green" title="E23">A3</font></i></a>, <a class="ref" href="amistd_1.html#D9" title="AMISTD_1:def.9">AMISTD_1:def 9</a></i>;<br/>


</div>
