<?xml version="1.0"?>
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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>;<br/>

<b>set </b><font color="Maroon" title="c2">S1</font> =  <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">NW-corner</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K21" title="PSCOMP_1:func.21">NE-corner</a> <font color="Maroon" title="c1">C</font></span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c3">S2</font> =  <a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K21" title="PSCOMP_1:func.21">NE-corner</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">SE-corner</a> <font color="Maroon" title="c1">C</font></span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c4">S3</font> =  <a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">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">SW-corner</a> <font color="Maroon" title="c1">C</font></span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c5">S4</font> =  <a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K19" title="PSCOMP_1:func.19">SW-corner</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K20" title="PSCOMP_1:func.20">NW-corner</a> <font color="Maroon" title="c1">C</font></span>)</span>;<br/>
<a NAME="E1:81"/><i><font color="Green" title="E61">A1</font></i>: 
 <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> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p3">(<span class="default"><a href="pscomp_1.html#K20" title="PSCOMP_1:func.20">NW-corner</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K21" title="PSCOMP_1:func.21">NE-corner</a> <font color="Maroon" title="c1">C</font></span>)</span></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p3">(<span class="default"><a href="pscomp_1.html#K21" title="PSCOMP_1:func.21">NE-corner</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">SE-corner</a> <font color="Maroon" title="c1">C</font></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p3">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">SE-corner</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K19" title="PSCOMP_1:func.19">SW-corner</a> <font color="Maroon" title="c1">C</font></span>)</span></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p3">(<span class="default"><a href="pscomp_1.html#K19" title="PSCOMP_1:func.19">SW-corner</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K20" title="PSCOMP_1:func.20">NW-corner</a> <font color="Maroon" title="c1">C</font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="sprect_1.html#T43" target="_self" title="SPRECT_1:th.43">Th43</a></i>;<br/>
<a NAME="E2:81"/><i><font color="Green" title="E62">A2</font></i>: 
 <a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">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#K16" title="PSCOMP_1:func.16">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 NAME="E3:81"/><i><font color="Green" title="E63">A3</font></i>: 
<span class="p1">(<span class="default"><a href="pscomp_1.html#K20" title="PSCOMP_1:func.20">NW-corner</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pscomp_1.html#K16" title="PSCOMP_1:func.16">N-bound</a> <font color="Maroon" title="c1">C</font>
 
<b>by </b><i><a class="ref" href="euclid.html#T56" title="EUCLID:th.56">EUCLID:56</a></i>;<br/>
<a NAME="E4:81"/><i><font color="Green" title="E64">A4</font></i>: 
<span class="p1">(<span class="default"><a href="pscomp_1.html#K21" title="PSCOMP_1:func.21">NE-corner</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pscomp_1.html#K16" title="PSCOMP_1:func.16">N-bound</a> <font color="Maroon" title="c1">C</font>
 
<b>by </b><i><a class="ref" href="euclid.html#T56" title="EUCLID:th.56">EUCLID:56</a></i>;<br/>
<a NAME="E5:81"/><i><font color="Green" title="E65">A5</font></i>: 
<span class="p1">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">SE-corner</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">S-bound</a> <font color="Maroon" title="c1">C</font>
 
<b>by </b><i><a class="ref" href="euclid.html#T56" title="EUCLID:th.56">EUCLID:56</a></i>;<br/>
<a NAME="E6:81"/><i><font color="Green" title="E66">A6</font></i>: 
<span class="p1">(<span class="default"><a href="pscomp_1.html#K19" title="PSCOMP_1:func.19">SW-corner</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">S-bound</a> <font color="Maroon" title="c1">C</font>
 
<b>by </b><i><a class="ref" href="euclid.html#T56" title="EUCLID:th.56">EUCLID:56</a></i>;<br/>
<a NAME="E7:81"/><i><font color="Green" title="E67">A7</font></i>: 
 <a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">S-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K21" title="PSCOMP_1:func.21">NE-corner</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">SE-corner</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#K18" title="PSCOMP_1:func.18">S-bound</a> <font color="Maroon" title="c1">C</font>
 
<b>by </b><i><a class="txt" href="sprect_1.html#E2:81"><i><font color="Green" title="E62">A2</font></i></a>, <a class="txt" href="sprect_1.html#E4:81"><i><font color="Green" title="E64">A4</font></i></a>, <a class="txt" href="sprect_1.html#E5:81"><i><font color="Green" title="E65">A5</font></i></a>, <a class="ref" href="sprect_1.html#T63" target="_self" title="SPRECT_1:th.63">Th63</a></i>;<br/>
<a NAME="E8:81"/><i><font color="Green" title="E68">A8</font></i>: 
 <a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">S-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K19" title="PSCOMP_1:func.19">SW-corner</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K20" title="PSCOMP_1:func.20">NW-corner</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#K18" title="PSCOMP_1:func.18">S-bound</a> <font color="Maroon" title="c1">C</font>
 
<b>by </b><i><a class="txt" href="sprect_1.html#E2:81"><i><font color="Green" title="E62">A2</font></i></a>, <a class="txt" href="sprect_1.html#E3:81"><i><font color="Green" title="E63">A3</font></i></a>, <a class="txt" href="sprect_1.html#E6:81"><i><font color="Green" title="E66">A6</font></i></a>, <a class="ref" href="sprect_1.html#T63" target="_self" title="SPRECT_1:th.63">Th63</a></i>;<br/>
<a NAME="E9:81"/><i><font color="Green" title="E69">A9</font></i>: 
<span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K20" title="PSCOMP_1:func.20">NW-corner</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K21" title="PSCOMP_1:func.21">NE-corner</a> <font color="Maroon" title="c1">C</font></span>)</span></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K21" title="PSCOMP_1:func.21">NE-corner</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">SE-corner</a> <font color="Maroon" title="c1">C</font></span>)</span></span>)</span> is <a href="compts_1.html#V6" title="COMPTS_1:attr.6">compact</a>
 
<b>by </b><i><a class="ref" href="compts_1.html#T19" title="COMPTS_1:th.19">COMPTS_1:19</a></i>;<br/>
<i><font color="Green" title="E70">A10</font></i>:  <a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">S-bound</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p3">(<span class="default"><a href="pscomp_1.html#K20" title="PSCOMP_1:func.20">NW-corner</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K21" title="PSCOMP_1:func.21">NE-corner</a> <font color="Maroon" title="c1">C</font></span>)</span></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p3">(<span class="default"><a href="pscomp_1.html#K21" title="PSCOMP_1:func.21">NE-corner</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">SE-corner</a> <font color="Maroon" title="c1">C</font></span>)</span></span>)</span></span>)</span> = 
 <a href="xxreal_0.html#K3" title="XXREAL_0:func.3">min</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">S-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p3">(<span class="default"><a href="pscomp_1.html#K20" title="PSCOMP_1:func.20">NW-corner</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K21" title="PSCOMP_1:func.21">NE-corner</a> <font color="Maroon" title="c1">C</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">S-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p3">(<span class="default"><a href="pscomp_1.html#K21" title="PSCOMP_1:func.21">NE-corner</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">SE-corner</a> <font color="Maroon" title="c1">C</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="sprect_1.html#T55" target="_self" title="SPRECT_1:th.55">Th55</a></i>
<br/>.= 
 <a href="xxreal_0.html#K3" title="XXREAL_0:func.3">min</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K16" title="PSCOMP_1:func.16">N-bound</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">S-bound</a> <font color="Maroon" title="c1">C</font></span>)</span>
<b>by </b><i><a class="txt" href="sprect_1.html#E3:81"><i><font color="Green" title="E63">A3</font></i></a>, <a class="txt" href="sprect_1.html#E4:81"><i><font color="Green" title="E64">A4</font></i></a>, <a class="txt" href="sprect_1.html#E7:81"><i><font color="Green" title="E67">A7</font></i></a>, <a class="ref" href="sprect_1.html#T63" target="_self" title="SPRECT_1:th.63">Th63</a></i>
<br/>.= 
 <a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">S-bound</a> <font color="Maroon" title="c1">C</font>
<b>by </b><i><a class="txt" href="sprect_1.html#E2:81"><i><font color="Green" title="E62">A2</font></i></a>, <a class="ref" href="xxreal_0.html#D8" title="XXREAL_0:def.8">XXREAL_0:def 8</a></i>
;<br/>
<a NAME="E11:81"/><i><font color="Green" title="E71">A11</font></i>: 
<span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">SE-corner</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K19" title="PSCOMP_1:func.19">SW-corner</a> <font color="Maroon" title="c1">C</font></span>)</span></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K19" title="PSCOMP_1:func.19">SW-corner</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K20" title="PSCOMP_1:func.20">NW-corner</a> <font color="Maroon" title="c1">C</font></span>)</span></span>)</span> is <a href="compts_1.html#V6" title="COMPTS_1:attr.6">compact</a>
 
<b>by </b><i><a class="ref" href="compts_1.html#T19" title="COMPTS_1:th.19">COMPTS_1:19</a></i>;<br/>
 <a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">S-bound</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p3">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">SE-corner</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K19" title="PSCOMP_1:func.19">SW-corner</a> <font color="Maroon" title="c1">C</font></span>)</span></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p3">(<span class="default"><a href="pscomp_1.html#K19" title="PSCOMP_1:func.19">SW-corner</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K20" title="PSCOMP_1:func.20">NW-corner</a> <font color="Maroon" title="c1">C</font></span>)</span></span>)</span></span>)</span> = 
 <a href="xxreal_0.html#K3" title="XXREAL_0:func.3">min</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">S-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p3">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">SE-corner</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K19" title="PSCOMP_1:func.19">SW-corner</a> <font color="Maroon" title="c1">C</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">S-bound</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p3">(<span class="default"><a href="pscomp_1.html#K19" title="PSCOMP_1:func.19">SW-corner</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K20" title="PSCOMP_1:func.20">NW-corner</a> <font color="Maroon" title="c1">C</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="sprect_1.html#T55" target="_self" title="SPRECT_1:th.55">Th55</a></i>
<br/>.= 
 <a href="xxreal_0.html#K3" title="XXREAL_0:func.3">min</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">S-bound</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">S-bound</a> <font color="Maroon" title="c1">C</font></span>)</span>
<b>by </b><i><a class="txt" href="sprect_1.html#E5:81"><i><font color="Green" title="E65">A5</font></i></a>, <a class="txt" href="sprect_1.html#E6:81"><i><font color="Green" title="E66">A6</font></i></a>, <a class="txt" href="sprect_1.html#E8:81"><i><font color="Green" title="E68">A8</font></i></a>, <a class="ref" href="sprect_1.html#T63" target="_self" title="SPRECT_1:th.63">Th63</a></i>
<br/>.= 
 <a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">S-bound</a> <font color="Maroon" title="c1">C</font>

;<br/>
<b>hence </b> <a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">S-bound</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="xxreal_0.html#K3" title="XXREAL_0:func.3">min</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">S-bound</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">S-bound</a> <font color="Maroon" title="c1">C</font></span>)</span>
<b>by </b><i><a class="txt" href="sprect_1.html#E1:81"><i><font color="Green" title="E61">A1</font></i></a>, <a class="txt" href="sprect_1.html#E9:81"><i><font color="Green" title="E69">A9</font></i></a>, <a class="txt" href="sprect_1.html#E10:81"><i><font color="Green" title="E70">A10</font></i></a>, <a class="txt" href="sprect_1.html#E11:81"><i><font color="Green" title="E71">A11</font></i></a>, <a class="ref" href="sprect_1.html#T55" target="_self" title="SPRECT_1:th.55">Th55</a></i>
<br/>.= 
 <a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">S-bound</a> <font color="Maroon" title="c1">C</font>

;<br/><br/>


</div>
