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<b>let </b><font color="Maroon" title="c1">C</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="compts_1.html#V6" title="COMPTS_1:attr.6">compact</a> <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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="pscomp_1.html#K29" title="PSCOMP_1:func.29">E-max</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <span class="p2">(<span class="default"><a href="sprect_1.html#K1" title="SPRECT_1:func.1">SpStSeq</a> <font color="Maroon" title="c1">C</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pscomp_1.html#K19" title="PSCOMP_1:func.19">NE-corner</a> <font color="Maroon" title="c1">C</font></span><br/>

<b>set </b><font color="Maroon" title="c2">X</font> =  <a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <span class="p1">(<span class="default"><a href="sprect_1.html#K1" title="SPRECT_1:func.1">SpStSeq</a> <font color="Maroon" title="c1">C</font></span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c3">S</font> =  <a href="pscomp_1.html#K23" title="PSCOMP_1:func.23">E-most</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <span class="p2">(<span class="default"><a href="sprect_1.html#K1" title="SPRECT_1:func.1">SpStSeq</a> <font color="Maroon" title="c1">C</font></span>)</span></span>)</span>;<br/>
<a NAME="E1:101"/><i><font color="Green" title="E80">A1</font></i>: 
 <a href="pscomp_1.html#K23" title="PSCOMP_1:func.23">E-most</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <span class="p2">(<span class="default"><a href="sprect_1.html#K1" title="SPRECT_1:func.1">SpStSeq</a> <font color="Maroon" title="c1">C</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K20" title="PSCOMP_1:func.20">SE-corner</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K19" title="PSCOMP_1:func.19">NE-corner</a> <font color="Maroon" title="c1">C</font></span>)</span>
 
<b>by </b><i><a class="ref" href="sprect_1.html#T77" target="_self" title="SPRECT_1:th.77">Th77</a></i>;<br/>
<a NAME="E2:101"/><i><font color="Green" title="E81">A2</font></i>: 
 <a href="pscomp_1.html#K16" title="PSCOMP_1:func.16">S-bound</a> <font color="Maroon" title="c1">C</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="pscomp_1.html#K14" title="PSCOMP_1:func.14">N-bound</a> <font color="Maroon" title="c1">C</font>
 
<b>by </b><i><a class="ref" href="sprect_1.html#T24" target="_self" title="SPRECT_1:th.24">Th24</a></i>;<br/>
 <a href="pscomp_1.html#K9" title="PSCOMP_1:func.9">sup</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K12" title="PSCOMP_1:func.12">proj2</a>  <a href="pscomp_1.html#K10" title="PSCOMP_1:func.10">||</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K23" title="PSCOMP_1:func.23">E-most</a> <span class="p3">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <span class="p4">(<span class="default"><a href="sprect_1.html#K1" title="SPRECT_1:func.1">SpStSeq</a> <font color="Maroon" title="c1">C</font></span>)</span></span>)</span></span>)</span></span>)</span> = 
 <a href="pscomp_1.html#K2" title="PSCOMP_1:func.2">sup</a> <span class="p1">(<span class="default"><a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K12" title="PSCOMP_1:func.12">proj2</a>  <a href="pscomp_1.html#K10" title="PSCOMP_1:func.10">||</a> <span class="p3">(<span class="default"><a href="pscomp_1.html#K23" title="PSCOMP_1:func.23">E-most</a> <span class="p4">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <span class="p5">(<span class="default"><a href="sprect_1.html#K1" title="SPRECT_1:func.1">SpStSeq</a> <font color="Maroon" title="c1">C</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="funct_2.html#T45" title="FUNCT_2:th.45">FUNCT_2:45</a></i>
<br/>.= 
 <a href="pscomp_1.html#K2" title="PSCOMP_1:func.2">sup</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K12" title="PSCOMP_1:func.12">proj2</a>  <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K23" title="PSCOMP_1:func.23">E-most</a> <span class="p3">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <span class="p4">(<span class="default"><a href="sprect_1.html#K1" title="SPRECT_1:func.1">SpStSeq</a> <font color="Maroon" title="c1">C</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="relat_1.html#T148" title="RELAT_1:th.148">RELAT_1:148</a></i>
<br/>.= 
 <a href="pscomp_1.html#K2" title="PSCOMP_1:func.2">sup</a> <span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K16" title="PSCOMP_1:func.16">S-bound</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K14" title="PSCOMP_1:func.14">N-bound</a> <font color="Maroon" title="c1">C</font></span>)</span></span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span>
<b>by </b><i><a class="txt" href="sprect_1.html#E1:101"><i><font color="Green" title="E80">A1</font></i></a>, <a class="ref" href="sprect_1.html#T80" target="_self" title="SPRECT_1:th.80">Th80</a></i>
<br/>.= 
 <a href="pscomp_1.html#K14" title="PSCOMP_1:func.14">N-bound</a> <font color="Maroon" title="c1">C</font>
<b>by </b><i><a class="txt" href="sprect_1.html#E2:101"><i><font color="Green" title="E81">A2</font></i></a>, <a class="ref" href="jordan5a.html#T20" title="JORDAN5A:th.20">JORDAN5A:20</a></i>
;<br/>
<b>hence </b><a NAME="E4:101"/>
 <a href="pscomp_1.html#K29" title="PSCOMP_1:func.29">E-max</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <span class="p2">(<span class="default"><a href="sprect_1.html#K1" title="SPRECT_1:func.1">SpStSeq</a> <font color="Maroon" title="c1">C</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pscomp_1.html#K19" title="PSCOMP_1:func.19">NE-corner</a> <font color="Maroon" title="c1">C</font>
 <b>by </b><i><a class="ref" href="sprect_1.html#T69" target="_self" title="SPRECT_1:th.69">Th69</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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