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<b>let </b><font color="Maroon">c<sub>1</sub></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/>

<i><font color="Green">E91</font></i>: <span class="p1">(<span class="default"><a href="pscomp_1.html#K19" target="_self">SW-corner</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  = 
 <a href="pscomp_1.html#K18" target="_self">S-bound</a> <font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="ref" href="pscomp_1.html#T73" target="_self">Th73</a></i>
<br/>.= 
 <a href="pscomp_1.html#K10" target="_self">inf</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>

;<br/>
<b>set </b><font color="Maroon">c<sub>2</sub></font> =  <a href="pscomp_1.html#K23" target="_self">W-most</a> <font color="Maroon">c<sub>1</sub></font>;<br/>
<a NAME="E2:126"/><i><font color="Green">E92</font></i>: 
<span class="p1">(<span class="default"><a href="pscomp_1.html#K27" target="_self">W-min</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#K10" target="_self">inf</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> <span class="p2">(<span class="default"><a href="pscomp_1.html#K23" target="_self">W-most</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="pscomp_1.html#T86" target="_self">Th86</a></i>;<br/>
<a NAME="E3:126"/><i><font color="Green">E93</font></i>: 
<span class="p1">(<span class="default"><a href="pscomp_1.html#K28" target="_self">W-max</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#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> <span class="p2">(<span class="default"><a href="pscomp_1.html#K23" target="_self">W-most</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="pscomp_1.html#T86" target="_self">Th86</a></i>;<br/>
<i><font color="Green">E94</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#K22">`2</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="pscomp_1.html#T75" target="_self">Th75</a></i>
<br/>.= 
 <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>
<b>by </b><i><a class="ref" href="pscomp_1.html#D31" target="_self">Def31</a></i>
;<br/>
<a NAME="E5:126"/><i><font color="Green">E95</font></i>: 
 <a href="pscomp_1.html#K23" target="_self">W-most</a> <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T17">XBOOLE_1:17</a></i>;<br/>
<a NAME="E6:126"/><b>then </b><i><font color="Green">E96</font></i>: 
<span class="p1">(<span class="default"><a href="pscomp_1.html#K19" target="_self">SW-corner</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K27" target="_self">W-min</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> 
 
<b>by </b><i><a class="txt" href="pscomp_1.html#E1:126"><i><font color="Green">E91</font></i></a>, <a class="txt" href="pscomp_1.html#E2:126"><i><font color="Green">E92</font></i></a>, <a class="ref" href="pscomp_1.html#T62" target="_self">Th62</a></i>;<br/>
<a NAME="E7:126"/><i><font color="Green">E97</font></i>: 
<span class="p1">(<span class="default"><a href="pscomp_1.html#K27" target="_self">W-min</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K28" target="_self">W-max</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> 
 
<b>by </b><i><a class="txt" href="pscomp_1.html#E2:126"><i><font color="Green">E92</font></i></a>, <a class="txt" href="pscomp_1.html#E3:126"><i><font color="Green">E93</font></i></a>, <a class="ref" href="pscomp_1.html#T53" target="_self">Th53</a></i>;<br/>
<a NAME="E8:126"/><i><font color="Green">E98</font></i>: 
<span class="p1">(<span class="default"><a href="pscomp_1.html#K28" target="_self">W-max</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</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> <a href="euclid.html#K22">`2</a> 
 
<b>by </b><i><a class="txt" href="pscomp_1.html#E3:126"><i><font color="Green">E93</font></i></a>, <a class="txt" href="pscomp_1.html#E4:126"><i><font color="Green">E94</font></i></a>, <a class="txt" href="pscomp_1.html#E5:126"><i><font color="Green">E95</font></i></a>, <a class="ref" href="pscomp_1.html#T63" target="_self">Th63</a></i>;<br/>
<b>thus </b><a NAME="E9:126"/>
<span class="p1">(<span class="default"><a href="pscomp_1.html#K19" target="_self">SW-corner</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K27" target="_self">W-min</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> 
 <b>by </b><i><a class="txt" href="pscomp_1.html#E1:126"><i><font color="Green">E91</font></i></a>, <a class="txt" href="pscomp_1.html#E2:126"><i><font color="Green">E92</font></i></a>, <a class="txt" href="pscomp_1.html#E5:126"><i><font color="Green">E95</font></i></a>, <a class="ref" href="pscomp_1.html#T62" target="_self">Th62</a></i>;<br/>

<b>thus </b><a NAME="E10:126"/>
<span class="p1">(<span class="default"><a href="pscomp_1.html#K19" target="_self">SW-corner</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K28" target="_self">W-max</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> 
 <b>by </b><i><a class="txt" href="pscomp_1.html#E6:126"><i><font color="Green">E96</font></i></a>, <a class="txt" href="pscomp_1.html#E7:126"><i><font color="Green">E97</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/>

<b>hence </b><a NAME="E11:126"/>
<span class="p1">(<span class="default"><a href="pscomp_1.html#K19" target="_self">SW-corner</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</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> <a href="euclid.html#K22">`2</a> 
 <b>by </b><i><a class="txt" href="pscomp_1.html#E8:126"><i><font color="Green">E98</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/>

<b>thus </b><a NAME="E12:126"/>
<span class="p1">(<span class="default"><a href="pscomp_1.html#K27" target="_self">W-min</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K28" target="_self">W-max</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> 
 <b>by </b><i><a class="txt" href="pscomp_1.html#E2:126"><i><font color="Green">E92</font></i></a>, <a class="txt" href="pscomp_1.html#E3:126"><i><font color="Green">E93</font></i></a>, <a class="ref" href="pscomp_1.html#T53" target="_self">Th53</a></i>;<br/>

<b>thus </b><a NAME="E13:126"/>
<span class="p1">(<span class="default"><a href="pscomp_1.html#K27" target="_self">W-min</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</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> <a href="euclid.html#K22">`2</a> 
 <b>by </b><i><a class="txt" href="pscomp_1.html#E7:126"><i><font color="Green">E97</font></i></a>, <a class="txt" href="pscomp_1.html#E8:126"><i><font color="Green">E98</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/>

<b>thus </b><a NAME="E14:126"/>
<span class="p1">(<span class="default"><a href="pscomp_1.html#K28" target="_self">W-max</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</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> <a href="euclid.html#K22">`2</a> 
 <b>by </b><i><a class="txt" href="pscomp_1.html#E3:126"><i><font color="Green">E93</font></i></a>, <a class="txt" href="pscomp_1.html#E4:126"><i><font color="Green">E94</font></i></a>, <a class="txt" href="pscomp_1.html#E5:126"><i><font color="Green">E95</font></i></a>, <a class="ref" href="pscomp_1.html#T63" target="_self">Th63</a></i>;<br/>


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