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<a NAME="E1:123_2_1"/><i><font color="Green">E87</font></i>: 
( <span class="p1">(<span class="default"><a href="pscomp_1.html#K20" target="_self">NW-corner</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="hidden.html#R1">=</a>  <a href="pscomp_1.html#K15" target="_self">W-bound</a> <font color="Maroon">c<sub>1</sub></font> &amp; <span class="p1">(<span class="default"><a href="pscomp_1.html#K21" target="_self">NE-corner</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="hidden.html#R1">=</a>  <a href="pscomp_1.html#K17" target="_self">E-bound</a> <font color="Maroon">c<sub>1</sub></font> &amp; <span class="p1">(<span class="default"><a href="pscomp_1.html#K20" target="_self">NW-corner</a> <font color="Maroon">c<sub>1</sub></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">c<sub>1</sub></font> &amp; <span class="p1">(<span class="default"><a href="pscomp_1.html#K21" target="_self">NE-corner</a> <font color="Maroon">c<sub>1</sub></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">c<sub>1</sub></font> )
 
<b>by </b><i><a class="ref" href="euclid.html#T56">EUCLID:56</a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>2</sub></font> = <a href="pscomp_1.html#K14" target="_self">proj2</a>  <a href="pscomp_1.html#K12" target="_self">||</a> <font color="Maroon">c<sub>1</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>3</sub></font> = the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K3">|</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>;<br/>
<a NAME="E2:123_2_1"/><i><font color="Green">E88</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K3">|</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="pre_topc.html#T29">PRE_TOPC:29</a></i>;<br/>
<a NAME="E3:123_2_1"/><i><font color="Green">E89</font></i>: 
 <a href="pscomp_1.html#K11" target="_self">sup</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K14" target="_self">proj2</a>  <a href="pscomp_1.html#K12" target="_self">||</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="pscomp_1.html#K2" target="_self">sup</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K14" target="_self">proj2</a>  <a href="pscomp_1.html#K12" target="_self">||</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="relset_1.html#K10">.:</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K3">|</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="pscomp_1.html#D21" target="_self">Def21</a></i>;<br/>
<a NAME="E4:123_2_1"/>
<span class="p1">(<span class="default"><a href="pscomp_1.html#K14" target="_self">proj2</a>  <a href="pscomp_1.html#K12" target="_self">||</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="relset_1.html#K10">.:</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K3">|</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> is <a href="pscomp_1.html#V1" target="_self">with_max</a>
 
<b>by </b><i><a class="ref" href="pscomp_1.html#D14" target="_self">Def14</a></i>;<br/>
<a NAME="E5:123_2_1"/><b>then </b>
 <a href="pscomp_1.html#K2" target="_self">sup</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K14" target="_self">proj2</a>  <a href="pscomp_1.html#K12" target="_self">||</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="relset_1.html#K10">.:</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K3">|</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K14" target="_self">proj2</a>  <a href="pscomp_1.html#K12" target="_self">||</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="relset_1.html#K10">.:</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K3">|</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="pscomp_1.html#D3" target="_self">Def3</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>4</sub></font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E7:123_2_1"/><i><font color="Green">E90</font></i>: 
( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K3">|</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K3">|</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> &amp;  <a href="pscomp_1.html#K2" target="_self">sup</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K14" target="_self">proj2</a>  <a href="pscomp_1.html#K12" target="_self">||</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="relset_1.html#K10">.:</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K3">|</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K14" target="_self">proj2</a>  <a href="pscomp_1.html#K12" target="_self">||</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="ref" href="funct_2.html#T115">FUNCT_2:115</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>4</sub></font> as   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <b>by </b><i><a class="txt" href="pscomp_1.html#E2:123_2_1"><i><font color="Green">E88</font></i></a>, <a class="txt" href="pscomp_1.html#E7:123_2_1"><i><font color="Green">E90</font></i></a></i>;<br/>
<a NAME="E9:123_2_1"/><i><font color="Green">E91</font></i>: 
<span class="p1">(<span class="default"><a href="pscomp_1.html#K14" target="_self">proj2</a>  <a href="pscomp_1.html#K12" target="_self">||</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> <a href="euclid.html#K22">`2</a> 
 
<b>by </b><i><a class="txt" href="pscomp_1.html#E2:123_2_1"><i><font color="Green">E88</font></i></a>, <a class="txt" href="pscomp_1.html#E7:123_2_1"><i><font color="Green">E90</font></i></a>, <a class="ref" href="pscomp_1.html#T70" target="_self">Th70</a></i>;<br/>
<a NAME="E10:123_2_1"/>
(  <a href="pscomp_1.html#K15" target="_self">W-bound</a> <font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>5</sub></font> <a href="euclid.html#K21">`1</a>  &amp; <font color="Maroon">c<sub>5</sub></font> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#R1">&lt;=</a>  <a href="pscomp_1.html#K17" target="_self">E-bound</a> <font color="Maroon">c<sub>1</sub></font> )
 
<b>by </b><i><a class="txt" href="pscomp_1.html#E2:123_2_1"><i><font color="Green">E88</font></i></a>, <a class="txt" href="pscomp_1.html#E7:123_2_1"><i><font color="Green">E90</font></i></a>, <a class="ref" href="pscomp_1.html#T71" target="_self">Th71</a></i>;<br/>
<a NAME="E11:123_2_1"/><b>then </b>
<font color="Maroon">c<sub>5</sub></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">c<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K21" target="_self">NE-corner</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="pscomp_1.html#E1:123_2_1"><i><font color="Green">E87</font></i></a>, <a class="txt" href="pscomp_1.html#E3:123_2_1"><i><font color="Green">E89</font></i></a>, <a class="txt" href="pscomp_1.html#E7:123_2_1"><i><font color="Green">E90</font></i></a>, <a class="txt" href="pscomp_1.html#E9:123_2_1"><i><font color="Green">E91</font></i></a>, <a class="ref" href="goboard7.html#T9">GOBOARD7:9</a></i>;<br/>
<b>hence </b><a NAME="E12:123_2_1"/>
( not  <a href="pscomp_1.html#K24" target="_self">N-most</a> <font color="Maroon">c<sub>1</sub></font> is <a href="xboole_0.html#V1">empty</a> &amp;  <a href="pscomp_1.html#K24" target="_self">N-most</a> <font color="Maroon">c<sub>1</sub></font> is <a href="compts_1.html#V6">compact</a> )
 <b>by </b><i><a class="txt" href="pscomp_1.html#E2:123_2_1"><i><font color="Green">E88</font></i></a>, <a class="txt" href="pscomp_1.html#E7:123_2_1"><i><font color="Green">E90</font></i></a>, <a class="ref" href="pscomp_1.html#T64" target="_self">Th64</a>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>


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