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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">E98</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="pscomp_1.html#K15" target="_self">W-bound</a> <font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="ref" href="pscomp_1.html#T74" target="_self">Th74</a></i>
<br/>.= 
 <a href="pscomp_1.html#K10" target="_self">inf</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K13" target="_self">proj1</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#K24" target="_self">N-most</a> <font color="Maroon">c<sub>1</sub></font>;<br/>
<a NAME="E2:134"/><i><font color="Green">E99</font></i>: 
<span class="p1">(<span class="default"><a href="pscomp_1.html#K29" target="_self">N-min</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#K10" target="_self">inf</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K13" target="_self">proj1</a>  <a href="pscomp_1.html#K12" target="_self">||</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K24" target="_self">N-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#T96" target="_self">Th96</a></i>;<br/>
<a NAME="E3:134"/><i><font color="Green">E100</font></i>: 
<span class="p1">(<span class="default"><a href="pscomp_1.html#K30" target="_self">N-max</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#K11" target="_self">sup</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K13" target="_self">proj1</a>  <a href="pscomp_1.html#K12" target="_self">||</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K24" target="_self">N-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#T96" target="_self">Th96</a></i>;<br/>
<i><font color="Green">E101</font></i>: <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="pscomp_1.html#K17" target="_self">E-bound</a> <font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="ref" href="pscomp_1.html#T76" target="_self">Th76</a></i>
<br/>.= 
 <a href="pscomp_1.html#K11" target="_self">sup</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K13" target="_self">proj1</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#D32" target="_self">Def32</a></i>
;<br/>
<a NAME="E5:134"/><i><font color="Green">E102</font></i>: 
 <a href="pscomp_1.html#K24" target="_self">N-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="E6:134"/><b>then </b><i><font color="Green">E103</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="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">c<sub>1</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> 
 
<b>by </b><i><a class="txt" href="pscomp_1.html#E1:134"><i><font color="Green">E98</font></i></a>, <a class="txt" href="pscomp_1.html#E2:134"><i><font color="Green">E99</font></i></a>, <a class="ref" href="pscomp_1.html#T62" target="_self">Th62</a></i>;<br/>
<a NAME="E7:134"/><i><font color="Green">E104</font></i>: 
<span class="p1">(<span class="default"><a href="pscomp_1.html#K29" target="_self">N-min</a> <font color="Maroon">c<sub>1</sub></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">c<sub>1</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> 
 
<b>by </b><i><a class="txt" href="pscomp_1.html#E2:134"><i><font color="Green">E99</font></i></a>, <a class="txt" href="pscomp_1.html#E3:134"><i><font color="Green">E100</font></i></a>, <a class="ref" href="pscomp_1.html#T53" target="_self">Th53</a></i>;<br/>
<a NAME="E8:134"/><i><font color="Green">E105</font></i>: 
<span class="p1">(<span class="default"><a href="pscomp_1.html#K30" target="_self">N-max</a> <font color="Maroon">c<sub>1</sub></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">c<sub>1</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> 
 
<b>by </b><i><a class="txt" href="pscomp_1.html#E3:134"><i><font color="Green">E100</font></i></a>, <a class="txt" href="pscomp_1.html#E4:134"><i><font color="Green">E101</font></i></a>, <a class="txt" href="pscomp_1.html#E5:134"><i><font color="Green">E102</font></i></a>, <a class="ref" href="pscomp_1.html#T63" target="_self">Th63</a></i>;<br/>
<b>thus </b><a NAME="E9:134"/>
<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="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">c<sub>1</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> 
 <b>by </b><i><a class="txt" href="pscomp_1.html#E1:134"><i><font color="Green">E98</font></i></a>, <a class="txt" href="pscomp_1.html#E2:134"><i><font color="Green">E99</font></i></a>, <a class="txt" href="pscomp_1.html#E5:134"><i><font color="Green">E102</font></i></a>, <a class="ref" href="pscomp_1.html#T62" target="_self">Th62</a></i>;<br/>

<b>thus </b><a NAME="E10:134"/>
<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="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">c<sub>1</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> 
 <b>by </b><i><a class="txt" href="pscomp_1.html#E6:134"><i><font color="Green">E103</font></i></a>, <a class="txt" href="pscomp_1.html#E7:134"><i><font color="Green">E104</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/>

<b>hence </b><a NAME="E11:134"/>
<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="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">c<sub>1</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> 
 <b>by </b><i><a class="txt" href="pscomp_1.html#E8:134"><i><font color="Green">E105</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/>

<b>thus </b><a NAME="E12:134"/>
<span class="p1">(<span class="default"><a href="pscomp_1.html#K29" target="_self">N-min</a> <font color="Maroon">c<sub>1</sub></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">c<sub>1</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> 
 <b>by </b><i><a class="txt" href="pscomp_1.html#E2:134"><i><font color="Green">E99</font></i></a>, <a class="txt" href="pscomp_1.html#E3:134"><i><font color="Green">E100</font></i></a>, <a class="ref" href="pscomp_1.html#T53" target="_self">Th53</a></i>;<br/>

<b>thus </b><a NAME="E13:134"/>
<span class="p1">(<span class="default"><a href="pscomp_1.html#K29" target="_self">N-min</a> <font color="Maroon">c<sub>1</sub></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">c<sub>1</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> 
 <b>by </b><i><a class="txt" href="pscomp_1.html#E7:134"><i><font color="Green">E104</font></i></a>, <a class="txt" href="pscomp_1.html#E8:134"><i><font color="Green">E105</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/>

<b>thus </b><a NAME="E14:134"/>
<span class="p1">(<span class="default"><a href="pscomp_1.html#K30" target="_self">N-max</a> <font color="Maroon">c<sub>1</sub></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">c<sub>1</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> 
 <b>by </b><i><a class="txt" href="pscomp_1.html#E3:134"><i><font color="Green">E100</font></i></a>, <a class="txt" href="pscomp_1.html#E4:134"><i><font color="Green">E101</font></i></a>, <a class="txt" href="pscomp_1.html#E5:134"><i><font color="Green">E102</font></i></a>, <a class="ref" href="pscomp_1.html#T63" target="_self">Th63</a></i>;<br/>


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