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<a NAME="E1:123_4_1"/><i><font color="Green" title="E83">A13</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">X</font></span>)</span> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pscomp_1.html#K15" title="PSCOMP_1:func.15">W-bound</a> <font color="Maroon" title="c1">X</font> &amp; <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">X</font></span>)</span> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pscomp_1.html#K17" title="PSCOMP_1:func.17">E-bound</a> <font color="Maroon" title="c1">X</font> &amp; <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">X</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">X</font> &amp; <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">X</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">X</font> )
 
<b>by </b><i><a class="ref" href="euclid.html#T56" title="EUCLID:th.56">EUCLID:56</a></i>;<br/>
<b>set </b><font color="Maroon" title="c2">p2X</font> = <a href="pscomp_1.html#K14" title="PSCOMP_1:func.14">proj2</a>  <a href="pscomp_1.html#K12" title="PSCOMP_1:func.12">||</a> <font color="Maroon" title="c1">X</font>;<br/>
<b>set </b><font color="Maroon" title="c3">c</font> = the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c1">X</font></span>)</span>;<br/>
<a NAME="E2:123_4_1"/><i><font color="Green" title="E84">A14</font></i>: 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">X</font>
 
<b>by </b><i><a class="ref" href="pre_topc.html#T29" title="PRE_TOPC:th.29">PRE_TOPC:29</a></i>;<br/>
<a NAME="E3:123_4_1"/>
<span class="p1">(<span class="default"><a href="pscomp_1.html#K14" title="PSCOMP_1:func.14">proj2</a>  <a href="pscomp_1.html#K12" title="PSCOMP_1:func.12">||</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c1">X</font></span>)</span> is <a href="pscomp_1.html#V2" title="PSCOMP_1:attr.2">with_min</a>
 
<b>by </b><i><a class="ref" href="pscomp_1.html#D15" target="_self" title="PSCOMP_1:def.15">Def15</a></i>;<br/>
<a NAME="E4:123_4_1"/><b>then </b>
 <a href="pscomp_1.html#K3" title="PSCOMP_1:func.3">inf</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K14" title="PSCOMP_1:func.14">proj2</a>  <a href="pscomp_1.html#K12" title="PSCOMP_1:func.12">||</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c1">X</font></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K14" title="PSCOMP_1:func.14">proj2</a>  <a href="pscomp_1.html#K12" title="PSCOMP_1:func.12">||</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c1">X</font></span>)</span>
 
<b>by </b><i><a class="ref" href="pscomp_1.html#D4" target="_self" title="PSCOMP_1:def.4">Def4</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c4">p</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E6:123_4_1"/><i><font color="Green" title="E85">A15</font></i>: 
( <font color="Maroon" title="c4">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c1">X</font></span>)</span> &amp; <font color="Maroon" title="c4">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c1">X</font></span>)</span> &amp;  <a href="pscomp_1.html#K3" title="PSCOMP_1:func.3">inf</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K14" title="PSCOMP_1:func.14">proj2</a>  <a href="pscomp_1.html#K12" title="PSCOMP_1:func.12">||</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c1">X</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K14" title="PSCOMP_1:func.14">proj2</a>  <a href="pscomp_1.html#K12" title="PSCOMP_1:func.12">||</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c4">p</font> )
 <b>by </b><i><a class="ref" href="funct_2.html#T115" title="FUNCT_2:th.115">FUNCT_2:115</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c5">p</font> = <font color="Maroon" title="c4">p</font> as   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> <b>by </b><i><a class="txt" href="pscomp_1.html#E2:123_4_1"><i><font color="Green" title="E84">A14</font></i></a>, <a class="txt" href="pscomp_1.html#E6:123_4_1"><i><font color="Green" title="E85">A15</font></i></a></i>;<br/>
<a NAME="E8:123_4_1"/><i><font color="Green" title="E86">A16</font></i>: 
<span class="p1">(<span class="default"><a href="pscomp_1.html#K14" title="PSCOMP_1:func.14">proj2</a>  <a href="pscomp_1.html#K12" title="PSCOMP_1:func.12">||</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c5">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">p</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> 
 
<b>by </b><i><a class="txt" href="pscomp_1.html#E2:123_4_1"><i><font color="Green" title="E84">A14</font></i></a>, <a class="txt" href="pscomp_1.html#E6:123_4_1"><i><font color="Green" title="E85">A15</font></i></a>, <a class="ref" href="pscomp_1.html#T70" target="_self" title="PSCOMP_1:th.70">Th70</a></i>;<br/>
<a NAME="E9:123_4_1"/>
(  <a href="pscomp_1.html#K15" title="PSCOMP_1:func.15">W-bound</a> <font color="Maroon" title="c1">X</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c5">p</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a>  &amp; <font color="Maroon" title="c5">p</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="pscomp_1.html#K17" title="PSCOMP_1:func.17">E-bound</a> <font color="Maroon" title="c1">X</font> )
 
<b>by </b><i><a class="txt" href="pscomp_1.html#E2:123_4_1"><i><font color="Green" title="E84">A14</font></i></a>, <a class="txt" href="pscomp_1.html#E6:123_4_1"><i><font color="Green" title="E85">A15</font></i></a>, <a class="ref" href="pscomp_1.html#T71" target="_self" title="PSCOMP_1:th.71">Th71</a></i>;<br/>
<a NAME="E10:123_4_1"/><b>then </b>
<font color="Maroon" title="c5">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <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">X</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">X</font></span>)</span>
 
<b>by </b><i><a class="txt" href="pscomp_1.html#E1:123_4_1"><i><font color="Green" title="E83">A13</font></i></a>, <a class="txt" href="pscomp_1.html#E6:123_4_1"><i><font color="Green" title="E85">A15</font></i></a>, <a class="txt" href="pscomp_1.html#E8:123_4_1"><i><font color="Green" title="E86">A16</font></i></a>, <a class="ref" href="goboard7.html#T9" title="GOBOARD7:th.9">GOBOARD7:9</a></i>;<br/>
<b>hence </b><a NAME="E11:123_4_1"/>
( not  <a href="pscomp_1.html#K26" title="PSCOMP_1:func.26">S-most</a> <font color="Maroon" title="c1">X</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp;  <a href="pscomp_1.html#K26" title="PSCOMP_1:func.26">S-most</a> <font color="Maroon" title="c1">X</font> is <a href="compts_1.html#V6" title="COMPTS_1:attr.6">compact</a> )
 <b>by </b><i><a class="txt" href="pscomp_1.html#E2:123_4_1"><i><font color="Green" title="E84">A14</font></i></a>, <a class="txt" href="pscomp_1.html#E6:123_4_1"><i><font color="Green" title="E85">A15</font></i></a>, <a class="ref" href="pscomp_1.html#T64" target="_self" title="PSCOMP_1:th.64">Th64</a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/>


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