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<b>let </b><font color="Maroon" title="c1">S</font> be   <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="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">S</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#K16" title="PSCOMP_1:func.16">NW-corner</a> <font color="Maroon" title="c1">S</font></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K17" title="PSCOMP_1:func.17">NE-corner</a> <font color="Maroon" title="c1">S</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#K17" title="PSCOMP_1:func.17">NE-corner</a> <font color="Maroon" title="c1">S</font></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">SE-corner</a> <font color="Maroon" title="c1">S</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#K18" title="PSCOMP_1:func.18">SE-corner</a> <font color="Maroon" title="c1">S</font></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K15" title="PSCOMP_1:func.15">SW-corner</a> <font color="Maroon" title="c1">S</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#K15" title="PSCOMP_1:func.15">SW-corner</a> <font color="Maroon" title="c1">S</font></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K16" title="PSCOMP_1:func.16">NW-corner</a> <font color="Maroon" title="c1">S</font></span>)</span></span>)</span></span>)</span></span><br/>

<a NAME="E1:47"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1"><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K16" title="PSCOMP_1:func.16">NW-corner</a> <font color="Maroon" title="c1">S</font></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K17" title="PSCOMP_1:func.17">NE-corner</a> <font color="Maroon" title="c1">S</font></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">SE-corner</a> <font color="Maroon" title="c1">S</font></span>)</span></span><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">*&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3
 
<b>by </b><i><a class="ref" href="finseq_1.html#T62" title="FINSEQ_1:th.62">FINSEQ_1:62</a></i>;<br/>
<a NAME="E2:47"/><b>then </b><i><font color="Green" title="E36">A1</font></i>: 
<span class="p1"><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K16" title="PSCOMP_1:func.16">NW-corner</a> <font color="Maroon" title="c1">S</font></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K17" title="PSCOMP_1:func.17">NE-corner</a> <font color="Maroon" title="c1">S</font></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">SE-corner</a> <font color="Maroon" title="c1">S</font></span>)</span></span><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">*&gt;</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2"><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="pscomp_1.html#K16" title="PSCOMP_1:func.16">NW-corner</a> <font color="Maroon" title="c1">S</font></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K17" title="PSCOMP_1:func.17">NE-corner</a> <font color="Maroon" title="c1">S</font></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">SE-corner</a> <font color="Maroon" title="c1">S</font></span>)</span></span><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">*&gt;</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">SE-corner</a> <font color="Maroon" title="c1">S</font>
 
<b>by </b><i><a class="ref" href="finseq_4.html#T27" title="FINSEQ_4:th.27">FINSEQ_4:27</a></i>;<br/>
<a NAME="E3:47"/>
<span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K15" title="PSCOMP_1:func.15">SW-corner</a> <font color="Maroon" title="c1">S</font></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K16" title="PSCOMP_1:func.16">NW-corner</a> <font color="Maroon" title="c1">S</font></span>)</span></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pscomp_1.html#K15" title="PSCOMP_1:func.15">SW-corner</a> <font color="Maroon" title="c1">S</font>
 
<b>by </b><i><a class="ref" href="finseq_4.html#T26" title="FINSEQ_4:th.26">FINSEQ_4:26</a></i>;<br/>
<b>hence </b> <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">S</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <span class="p3"><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">&lt;*</a><span class="default"><span class="p4">(<span class="default"><a href="pscomp_1.html#K16" title="PSCOMP_1:func.16">NW-corner</a> <font color="Maroon" title="c1">S</font></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K17" title="PSCOMP_1:func.17">NE-corner</a> <font color="Maroon" title="c1">S</font></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">SE-corner</a> <font color="Maroon" title="c1">S</font></span>)</span></span><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">*&gt;</a></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#K18" title="PSCOMP_1:func.18">SE-corner</a> <font color="Maroon" title="c1">S</font></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K15" title="PSCOMP_1:func.15">SW-corner</a> <font color="Maroon" title="c1">S</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"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <span class="p2"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="pscomp_1.html#K15" title="PSCOMP_1:func.15">SW-corner</a> <font color="Maroon" title="c1">S</font></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K16" title="PSCOMP_1:func.16">NW-corner</a> <font color="Maroon" title="c1">S</font></span>)</span></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span></span>)</span>
<b>by </b><i><a class="txt" href="#E2:47"><i><font color="Green" title="E36">A1</font></i></a>, <a class="ref" href="sppol_2.html#T23" title="SPPOL_2:th.23">SPPOL_2:23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <span class="p3"><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">&lt;*</a><span class="default"><span class="p4">(<span class="default"><a href="pscomp_1.html#K16" title="PSCOMP_1:func.16">NW-corner</a> <font color="Maroon" title="c1">S</font></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K17" title="PSCOMP_1:func.17">NE-corner</a> <font color="Maroon" title="c1">S</font></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">SE-corner</a> <font color="Maroon" title="c1">S</font></span>)</span></span><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">*&gt;</a></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#K18" title="PSCOMP_1:func.18">SE-corner</a> <font color="Maroon" title="c1">S</font></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K15" title="PSCOMP_1:func.15">SW-corner</a> <font color="Maroon" title="c1">S</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"><a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K15" title="PSCOMP_1:func.15">SW-corner</a> <font color="Maroon" title="c1">S</font></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K16" title="PSCOMP_1:func.16">NW-corner</a> <font color="Maroon" title="c1">S</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="sppol_2.html#T21" title="SPPOL_2:th.21">SPPOL_2:21</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p4">(<span class="default"><a href="pscomp_1.html#K16" title="PSCOMP_1:func.16">NW-corner</a> <font color="Maroon" title="c1">S</font></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K17" title="PSCOMP_1:func.17">NE-corner</a> <font color="Maroon" title="c1">S</font></span>)</span></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p4">(<span class="default"><a href="pscomp_1.html#K17" title="PSCOMP_1:func.17">NE-corner</a> <font color="Maroon" title="c1">S</font></span>)</span>,<span class="p4">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">SE-corner</a> <font color="Maroon" title="c1">S</font></span>)</span></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#K18" title="PSCOMP_1:func.18">SE-corner</a> <font color="Maroon" title="c1">S</font></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K15" title="PSCOMP_1:func.15">SW-corner</a> <font color="Maroon" title="c1">S</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"><a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K15" title="PSCOMP_1:func.15">SW-corner</a> <font color="Maroon" title="c1">S</font></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K16" title="PSCOMP_1:func.16">NW-corner</a> <font color="Maroon" title="c1">S</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="sprect_1.html#T10" target="_self" title="SPRECT_1:th.10">Th10</a></i>
<br/>.= 
<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#K16" title="PSCOMP_1:func.16">NW-corner</a> <font color="Maroon" title="c1">S</font></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K17" title="PSCOMP_1:func.17">NE-corner</a> <font color="Maroon" title="c1">S</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#K17" title="PSCOMP_1:func.17">NE-corner</a> <font color="Maroon" title="c1">S</font></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">SE-corner</a> <font color="Maroon" title="c1">S</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#K18" title="PSCOMP_1:func.18">SE-corner</a> <font color="Maroon" title="c1">S</font></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K15" title="PSCOMP_1:func.15">SW-corner</a> <font color="Maroon" title="c1">S</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#K15" title="PSCOMP_1:func.15">SW-corner</a> <font color="Maroon" title="c1">S</font></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K16" title="PSCOMP_1:func.16">NW-corner</a> <font color="Maroon" title="c1">S</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xboole_1.html#T4" title="XBOOLE_1:th.4">XBOOLE_1:4</a></i>
;<br/> <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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