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<b>let </b><font color="Maroon">c<sub>2</sub></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">c<sub>3</sub></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" target="_self">standard</a>  <a href="ami_1.html#L1">AMI-Struct</a> of <font color="Maroon">c<sub>2</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></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">c<sub>3</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>5</sub></font> be   <a href="ami_1.html#NM2">Instruction-Location</a> of <font color="Maroon">c<sub>3</sub></font>;<br/>







<b>assume </b><a NAME="E1:87"/><i><font color="Green">E47</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/>

<b>consider </b><font color="Maroon">c<sub>6</sub></font> being  non <a href="xboole_0.html#V1">empty</a> <a href="finset_1.html#V1">finite</a> <a href="membered.html#V5">natural-membered</a>  <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:87"/><i><font color="Green">E48</font></i>: 
<font color="Maroon">c<sub>6</sub></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" target="_self">locnum</a> <font color="Olive">b<sub>1</sub></font></span>)</span> where B is    <a href="struct_0.html#M1">Element</a> of the <a href="ami_1.html#U2">Instruction-Locations</a> of <font color="Maroon">c<sub>3</sub></font> : <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>4</sub></font> </span>}</span> 
 <b>and </b><br/><a NAME="E4:87"/><i><font color="Green">E49</font></i>: 
 <a href="amistd_1.html#K10" target="_self">LastLoc</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="amistd_1.html#K5" target="_self">il.</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><a href="pre_circ.html#K1">max</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="amistd_1.html#D21" target="_self">Def21</a></i>;<br/>
<a NAME="E5:87"/><i><font color="Green">E50</font></i>: 
 <a href="amistd_1.html#K7" target="_self">locnum</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K10" target="_self">LastLoc</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="pre_circ.html#K1">max</a> <font color="Maroon">c<sub>6</sub></font>
 
<b>by </b><i><a class="txt" href="amistd_1.html#E4:87"><i><font color="Green">E49</font></i></a>, <a class="ref" href="amistd_1.html#D13" target="_self">Def13</a></i>;<br/>
<a NAME="E6:87"/>
 <a href="amistd_1.html#K7" target="_self">locnum</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>6</sub></font>
 
<b>by </b><i><a class="txt" href="amistd_1.html#E1:87"><i><font color="Green">E47</font></i></a>, <a class="txt" href="amistd_1.html#E3:87"><i><font color="Green">E48</font></i></a></i>;<br/>
<a NAME="E7:87"/><b>then </b>
 <a href="amistd_1.html#K7" target="_self">locnum</a> <font color="Maroon">c<sub>5</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="pre_circ.html#K1">max</a> <font color="Maroon">c<sub>6</sub></font>
 
<b>by </b><i><a class="ref" href="pre_circ.html#D1">PRE_CIRC:def 1</a></i>;<br/>
<b>hence </b><a NAME="E8:87"/>
<font color="Maroon">c<sub>5</sub></font> <a href="amistd_1.html#R1" target="_self">&lt;=</a>  <a href="amistd_1.html#K10" target="_self">LastLoc</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="amistd_1.html#E5:87"><i><font color="Green">E50</font></i></a>, <a class="ref" href="amistd_1.html#T29" target="_self">Th29</a></i>;<br/>


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