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<b>let </b><font color="Maroon" title="c1">P</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span>;<br/>

<b>assume </b><a NAME="E1:160"/><i><font color="Green" title="E111">A1</font></i>: 
 <a href="pscomp_1.html#K34" title="PSCOMP_1:func.34">S-min</a> <font color="Maroon" title="c1">P</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pscomp_1.html#K27" title="PSCOMP_1:func.27">W-min</a> <font color="Maroon" title="c1">P</font>
 ;<br/>

<a NAME="E2:160"/><i><font color="Green" title="E112">A2</font></i>: 
( <span class="p1">(<span class="default"><a href="pscomp_1.html#K34" title="PSCOMP_1:func.34">S-min</a> <font color="Maroon" title="c1">P</font></span>)</span> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">S-bound</a> <font color="Maroon" title="c1">P</font> &amp; <span class="p1">(<span class="default"><a href="pscomp_1.html#K27" title="PSCOMP_1:func.27">W-min</a> <font color="Maroon" title="c1">P</font></span>)</span> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pscomp_1.html#K15" title="PSCOMP_1:func.15">W-bound</a> <font color="Maroon" title="c1">P</font> &amp; <span class="p1">(<span class="default"><a href="pscomp_1.html#K19" title="PSCOMP_1:func.19">SW-corner</a> <font color="Maroon" title="c1">P</font></span>)</span> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pscomp_1.html#K15" title="PSCOMP_1:func.15">W-bound</a> <font color="Maroon" title="c1">P</font> &amp; <span class="p1">(<span class="default"><a href="pscomp_1.html#K19" title="PSCOMP_1:func.19">SW-corner</a> <font color="Maroon" title="c1">P</font></span>)</span> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">S-bound</a> <font color="Maroon" title="c1">P</font> )
 
<b>by </b><i><a class="txt" href="pscomp_1.html#E118"><i><font color="Green" title="E75">Lm10</font></i></a>, <a class="txt" href="pscomp_1.html#E119"><i><font color="Green" title="E76">Lm11</font></i></a>, <a class="txt" href="pscomp_1.html#E150"><i><font color="Green" title="E83">Lm18</font></i></a>, <a class="txt" href="pscomp_1.html#E186"><i><font color="Green" title="E104">Lm24</font></i></a></i>;<br/>
<a NAME="E3:160"/>
(  <a href="pscomp_1.html#K19" title="PSCOMP_1:func.19">SW-corner</a> <font color="Maroon" title="c1">P</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="pscomp_1.html#K19" title="PSCOMP_1:func.19">SW-corner</a> <font color="Maroon" title="c1">P</font></span>)</span> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="pscomp_1.html#K19" title="PSCOMP_1:func.19">SW-corner</a> <font color="Maroon" title="c1">P</font></span>)</span> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span></span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span> &amp;  <a href="pscomp_1.html#K34" title="PSCOMP_1:func.34">S-min</a> <font color="Maroon" title="c1">P</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="pscomp_1.html#K34" title="PSCOMP_1:func.34">S-min</a> <font color="Maroon" title="c1">P</font></span>)</span> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="pscomp_1.html#K34" title="PSCOMP_1:func.34">S-min</a> <font color="Maroon" title="c1">P</font></span>)</span> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span></span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span> )
 
<b>by </b><i><a class="ref" href="euclid.html#T57" title="EUCLID:th.57">EUCLID:57</a></i>;<br/>
<b>hence </b><a NAME="E4:160"/>
 <a href="pscomp_1.html#K34" title="PSCOMP_1:func.34">S-min</a> <font color="Maroon" title="c1">P</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pscomp_1.html#K19" title="PSCOMP_1:func.19">SW-corner</a> <font color="Maroon" title="c1">P</font>
 <b>by </b><i><a class="txt" href="pscomp_1.html#E1:160"><i><font color="Green" title="E111">A1</font></i></a>, <a class="txt" href="pscomp_1.html#E2:160"><i><font color="Green" title="E112">A2</font></i></a></i>;<br/>


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