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<b>let </b><font color="Maroon">X</font> be  non <a href="xboole_0.html#V1">empty</a> <a href="compts_1.html#V6">compact</a> <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>;<br/>

<a NAME="E1:137"/><i><font color="Green">E30</font></i>: 
( <span class="p1">(<span class="default"><a href="pscomp_1.html#K20" target="_self">NW-corner</a> <font color="Maroon">X</font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="hidden.html#R1">=</a>  <a href="pscomp_1.html#K16" target="_self">N-bound</a> <font color="Maroon">X</font> &amp; <span class="p1">(<span class="default"><a href="pscomp_1.html#K29" target="_self">N-min</a> <font color="Maroon">X</font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="hidden.html#R1">=</a>  <a href="pscomp_1.html#K16" target="_self">N-bound</a> <font color="Maroon">X</font> &amp; <span class="p1">(<span class="default"><a href="pscomp_1.html#K30" target="_self">N-max</a> <font color="Maroon">X</font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="hidden.html#R1">=</a>  <a href="pscomp_1.html#K16" target="_self">N-bound</a> <font color="Maroon">X</font> &amp; <span class="p1">(<span class="default"><a href="pscomp_1.html#K21" target="_self">NE-corner</a> <font color="Maroon">X</font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="hidden.html#R1">=</a>  <a href="pscomp_1.html#K16" target="_self">N-bound</a> <font color="Maroon">X</font> )
 
<b>by </b><i>, , </i>;<br/>
<a NAME="E2:137"/>
( <span class="p1">(<span class="default"><a href="pscomp_1.html#K20" target="_self">NW-corner</a> <font color="Maroon">X</font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K29" target="_self">N-min</a> <font color="Maroon">X</font></span>)</span> <a href="euclid.html#K21">`1</a>  &amp; <span class="p1">(<span class="default"><a href="pscomp_1.html#K20" target="_self">NW-corner</a> <font color="Maroon">X</font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K30" target="_self">N-max</a> <font color="Maroon">X</font></span>)</span> <a href="euclid.html#K21">`1</a>  &amp; <span class="p1">(<span class="default"><a href="pscomp_1.html#K29" target="_self">N-min</a> <font color="Maroon">X</font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K21" target="_self">NE-corner</a> <font color="Maroon">X</font></span>)</span> <a href="euclid.html#K21">`1</a>  &amp; <span class="p1">(<span class="default"><a href="pscomp_1.html#K30" target="_self">N-max</a> <font color="Maroon">X</font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K21" target="_self">NE-corner</a> <font color="Maroon">X</font></span>)</span> <a href="euclid.html#K21">`1</a>  )
 
<b>by </b><i/>;<br/>
<a NAME="E3:137"/><b>then </b>
(  <a href="pscomp_1.html#K29" target="_self">N-min</a> <font color="Maroon">X</font> <a href="hidden.html#R2">in</a>  <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K20" target="_self">NW-corner</a> <font color="Maroon">X</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K21" target="_self">NE-corner</a> <font color="Maroon">X</font></span>)</span> &amp;  <a href="pscomp_1.html#K30" target="_self">N-max</a> <font color="Maroon">X</font> <a href="hidden.html#R2">in</a>  <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K20" target="_self">NW-corner</a> <font color="Maroon">X</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K21" target="_self">NE-corner</a> <font color="Maroon">X</font></span>)</span> )
 
<b>by </b><i>, <a class="ref" href="goboard7.html#T9">GOBOARD7:9</a></i>;<br/>
<b>hence </b><a NAME="E4:137"/>
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K29" target="_self">N-min</a> <font color="Maroon">X</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K30" target="_self">N-max</a> <font color="Maroon">X</font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K20" target="_self">NW-corner</a> <font color="Maroon">X</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K21" target="_self">NE-corner</a> <font color="Maroon">X</font></span>)</span>
 <b>by </b><i><a class="ref" href="topreal1.html#T12">TOPREAL1:12</a></i>;<br/>


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