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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="E1:157"/><i><font color="Green" title="E111">A1</font></i>: 
 <a href="pscomp_1.html#K28" title="PSCOMP_1:func.28">W-max</a> <font color="Maroon" title="c1">P</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pscomp_1.html#K29" title="PSCOMP_1:func.29">N-min</a> <font color="Maroon" title="c1">P</font>
 ;<br/>

<a NAME="E2:157"/><i><font color="Green" title="E112">A2</font></i>: 
( <span class="p1">(<span class="default"><a href="pscomp_1.html#K28" title="PSCOMP_1:func.28">W-max</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#K29" title="PSCOMP_1:func.29">N-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#K16" title="PSCOMP_1:func.16">N-bound</a> <font color="Maroon" title="c1">P</font> &amp; <span class="p1">(<span class="default"><a href="pscomp_1.html#K20" title="PSCOMP_1:func.20">NW-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#K20" title="PSCOMP_1:func.20">NW-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#K16" title="PSCOMP_1:func.16">N-bound</a> <font color="Maroon" title="c1">P</font> )
 
<b>by </b><i><a class="txt" href="pscomp_1.html#E120"><i><font color="Green" title="E77">Lm12</font></i></a>, <a class="txt" href="pscomp_1.html#E121"><i><font color="Green" title="E78">Lm13</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#E162"><i><font color="Green" title="E90">Lm20</font></i></a></i>;<br/>
<a NAME="E3:157"/>
(  <a href="pscomp_1.html#K20" title="PSCOMP_1:func.20">NW-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#K20" title="PSCOMP_1:func.20">NW-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#K20" title="PSCOMP_1:func.20">NW-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#K28" title="PSCOMP_1:func.28">W-max</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#K28" title="PSCOMP_1:func.28">W-max</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#K28" title="PSCOMP_1:func.28">W-max</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="E4:157"/>
 <a href="pscomp_1.html#K28" title="PSCOMP_1:func.28">W-max</a> <font color="Maroon" title="c1">P</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pscomp_1.html#K20" title="PSCOMP_1:func.20">NW-corner</a> <font color="Maroon" title="c1">P</font>
 <b>by </b><i><a class="txt" href="pscomp_1.html#E1:157"><i><font color="Green" title="E111">A1</font></i></a>, <a class="txt" href="pscomp_1.html#E2:157"><i><font color="Green" title="E112">A2</font></i></a></i>;<br/>


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