<?xml version="1.0"?>
<div class="add">

<span class="kw">let </span><font color="Maroon" title="c1">X</font> be  non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="compts_1.html#V2" title="COMPTS_1:attr.2">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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="pscomp_1.html#K25" title="PSCOMP_1:func.25">S-min</a> <font color="Maroon" title="c1">X</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="pscomp_1.html#K17" title="PSCOMP_1:func.17">S-most</a> <font color="Maroon" title="c1">X</font> &amp;  <a href="pscomp_1.html#K24" title="PSCOMP_1:func.24">S-max</a> <font color="Maroon" title="c1">X</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="pscomp_1.html#K17" title="PSCOMP_1:func.17">S-most</a> <font color="Maroon" title="c1">X</font> )</span><br/>

<span class="kw">set </span><font color="Maroon" title="c2">p2W</font> = <a href="pscomp_1.html#K4" title="PSCOMP_1:func.4">proj1</a>  <a href="pscomp_1.html#K3" title="PSCOMP_1:func.3">|</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K17" title="PSCOMP_1:func.17">S-most</a> <font color="Maroon" title="c1">X</font></span>)</span>;<br/>
<span class="kw">set </span><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> <span class="p2">(<span class="default"><a href="pscomp_1.html#K17" title="PSCOMP_1:func.17">S-most</a> <font color="Maroon" title="c1">X</font></span>)</span></span>)</span>;<br/>
<a NAME="E1:144"/><span class="lab"><font color="Green" title="E48">A1</font></span>: 
( <span class="p1">(<span class="default"><a href="pscomp_1.html#K10" title="PSCOMP_1:func.10">SW-corner</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pscomp_1.html#K9" title="PSCOMP_1:func.9">S-bound</a> <font color="Maroon" title="c1">X</font> &amp; <span class="p1">(<span class="default"><a href="pscomp_1.html#K13" title="PSCOMP_1:func.13">SE-corner</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pscomp_1.html#K9" title="PSCOMP_1:func.9">S-bound</a> <font color="Maroon" title="c1">X</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T56" title="EUCLID:th.56">EUCLID:56</a></span>;<br/>
<a NAME="E2:144"/>
<span class="p1">(<span class="default"><a href="pscomp_1.html#K4" title="PSCOMP_1:func.4">proj1</a>  <a href="pscomp_1.html#K3" title="PSCOMP_1:func.3">|</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K17" title="PSCOMP_1:func.17">S-most</a> <font color="Maroon" title="c1">X</font></span>)</span></span>)</span> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</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> <span class="p2">(<span class="default"><a href="pscomp_1.html#K17" title="PSCOMP_1:func.17">S-most</a> <font color="Maroon" title="c1">X</font></span>)</span></span>)</span> is  <a href="measure6.html#V2" title="MEASURE6:attr.2">with_min</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="measure6.html#D20" title="MEASURE6:def.20">MEASURE6:def 20</a></span>;<br/>
<a NAME="E3:144"/><span class="kw">then </span>
 <a href="measure6.html#NK5" title="MEASURE6:NK.5">inf</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K4" title="PSCOMP_1:func.4">proj1</a>  <a href="pscomp_1.html#K3" title="PSCOMP_1:func.3">|</a> <span class="p3">(<span class="default"><a href="pscomp_1.html#K17" title="PSCOMP_1:func.17">S-most</a> <font color="Maroon" title="c1">X</font></span>)</span></span>)</span> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</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> <span class="p3">(<span class="default"><a href="pscomp_1.html#K17" title="PSCOMP_1:func.17">S-most</a> <font color="Maroon" title="c1">X</font></span>)</span></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#K4" title="PSCOMP_1:func.4">proj1</a>  <a href="pscomp_1.html#K3" title="PSCOMP_1:func.3">|</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K17" title="PSCOMP_1:func.17">S-most</a> <font color="Maroon" title="c1">X</font></span>)</span></span>)</span> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</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> <span class="p2">(<span class="default"><a href="pscomp_1.html#K17" title="PSCOMP_1:func.17">S-most</a> <font color="Maroon" title="c1">X</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="measure6.html#D10" title="MEASURE6:def.10">MEASURE6:def 10</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c4">p</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E5:144"/><span class="lab"><font color="Green" title="E49">A2</font></span>: 
<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> <span class="p2">(<span class="default"><a href="pscomp_1.html#K17" title="PSCOMP_1:func.17">S-most</a> <font color="Maroon" title="c1">X</font></span>)</span></span>)</span>
 <span class="kw">and </span><br/><a NAME="E6:144"/>
<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> <span class="p2">(<span class="default"><a href="pscomp_1.html#K17" title="PSCOMP_1:func.17">S-most</a> <font color="Maroon" title="c1">X</font></span>)</span></span>)</span>
 <span class="kw">and </span><br/><a NAME="E7:144"/><span class="lab"><font color="Green" title="E50">A3</font></span>: 
 <a href="measure6.html#NK5" title="MEASURE6:NK.5">inf</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K4" title="PSCOMP_1:func.4">proj1</a>  <a href="pscomp_1.html#K3" title="PSCOMP_1:func.3">|</a> <span class="p3">(<span class="default"><a href="pscomp_1.html#K17" title="PSCOMP_1:func.17">S-most</a> <font color="Maroon" title="c1">X</font></span>)</span></span>)</span> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</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> <span class="p3">(<span class="default"><a href="pscomp_1.html#K17" title="PSCOMP_1:func.17">S-most</a> <font color="Maroon" title="c1">X</font></span>)</span></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#K4" title="PSCOMP_1:func.4">proj1</a>  <a href="pscomp_1.html#K3" title="PSCOMP_1:func.3">|</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K17" title="PSCOMP_1:func.17">S-most</a> <font color="Maroon" title="c1">X</font></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c4">p</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#T115" title="FUNCT_2:th.115">FUNCT_2:115</a></span>;<br/>
<a NAME="E8:144"/><span class="lab"><font color="Green" title="E51">A4</font></span>: 
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> <span class="p2">(<span class="default"><a href="pscomp_1.html#K17" title="PSCOMP_1:func.17">S-most</a> <font color="Maroon" title="c1">X</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pscomp_1.html#K17" title="PSCOMP_1:func.17">S-most</a> <font color="Maroon" title="c1">X</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="pre_topc.html#T29" title="PRE_TOPC:th.29">PRE_TOPC:29</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><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> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:144"><span class="lab"><font color="Green" title="E49">A2</font></span></a></span>;<br/>
<a NAME="E10:144"/>
<font color="Maroon" title="c5">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rltopsp1.html#K1" title="RLTOPSP1:func.1">LSeg</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K10" title="PSCOMP_1:func.10">SW-corner</a> <font color="Maroon" title="c1">X</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K13" title="PSCOMP_1:func.13">SE-corner</a> <font color="Maroon" title="c1">X</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:144"><span class="lab"><font color="Green" title="E51">A4</font></span></a>, <a class="txt" href="#E5:144"><span class="lab"><font color="Green" title="E49">A2</font></span></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></span>;<br/>
<a NAME="E11:144"/><span class="kw">then </span><span class="lab"><font color="Green" title="E52">A5</font></span>: 
<font color="Maroon" title="c5">p</font> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pscomp_1.html#K9" title="PSCOMP_1:func.9">S-bound</a> <font color="Maroon" title="c1">X</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:144"><span class="lab"><font color="Green" title="E48">A1</font></span></a>, <a class="ref" href="goboard7.html#T6" title="GOBOARD7:th.6">GOBOARD7:6</a></span>;<br/>
<a NAME="E12:144"/><span class="lab"><font color="Green" title="E53">A6</font></span>: 
( <span class="p1">(<span class="default"><a href="pscomp_1.html#K10" title="PSCOMP_1:func.10">SW-corner</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pscomp_1.html#K9" title="PSCOMP_1:func.9">S-bound</a> <font color="Maroon" title="c1">X</font> &amp; <span class="p1">(<span class="default"><a href="pscomp_1.html#K13" title="PSCOMP_1:func.13">SE-corner</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pscomp_1.html#K9" title="PSCOMP_1:func.9">S-bound</a> <font color="Maroon" title="c1">X</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T56" title="EUCLID:th.56">EUCLID:56</a></span>;<br/>
<a NAME="E13:144"/>
<span class="p1">(<span class="default"><a href="pscomp_1.html#K4" title="PSCOMP_1:func.4">proj1</a>  <a href="pscomp_1.html#K3" title="PSCOMP_1:func.3">|</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K17" title="PSCOMP_1:func.17">S-most</a> <font color="Maroon" title="c1">X</font></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</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#K17" title="EUCLID:func.17">`1</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:144"><span class="lab"><font color="Green" title="E51">A4</font></span></a>, <a class="txt" href="#E5:144"><span class="lab"><font color="Green" title="E49">A2</font></span></a>, <a class="ref" href="pscomp_1.html#T69" target="_self" title="PSCOMP_1:th.69">Th69</a></span>;<br/>
<span class="kw">hence </span><a NAME="E14:144"/>
 <a href="pscomp_1.html#K25" title="PSCOMP_1:func.25">S-min</a> <font color="Maroon" title="c1">X</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="pscomp_1.html#K17" title="PSCOMP_1:func.17">S-most</a> <font color="Maroon" title="c1">X</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:144"><span class="lab"><font color="Green" title="E51">A4</font></span></a>, <a class="txt" href="#E5:144"><span class="lab"><font color="Green" title="E49">A2</font></span></a>, <a class="txt" href="#E7:144"><span class="lab"><font color="Green" title="E50">A3</font></span></a>, <a class="txt" href="#E11:144"><span class="lab"><font color="Green" title="E52">A5</font></span></a>, <a class="ref" href="euclid.html#T57" title="EUCLID:th.57">EUCLID:57</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="pscomp_1.html#K24" title="PSCOMP_1:func.24">S-max</a> <font color="Maroon" title="c1">X</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="pscomp_1.html#K17" title="PSCOMP_1:func.17">S-most</a> <font color="Maroon" title="c1">X</font></span><br/>

<a NAME="E15:144"/>
<span class="p1">(<span class="default"><a href="pscomp_1.html#K4" title="PSCOMP_1:func.4">proj1</a>  <a href="pscomp_1.html#K3" title="PSCOMP_1:func.3">|</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K17" title="PSCOMP_1:func.17">S-most</a> <font color="Maroon" title="c1">X</font></span>)</span></span>)</span> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</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> <span class="p2">(<span class="default"><a href="pscomp_1.html#K17" title="PSCOMP_1:func.17">S-most</a> <font color="Maroon" title="c1">X</font></span>)</span></span>)</span> is  <a href="measure6.html#V1" title="MEASURE6:attr.1">with_max</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="measure6.html#D19" title="MEASURE6:def.19">MEASURE6:def 19</a></span>;<br/>
<a NAME="E16:144"/><span class="kw">then </span>
 <a href="measure6.html#NK4" title="MEASURE6:NK.4">sup</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K4" title="PSCOMP_1:func.4">proj1</a>  <a href="pscomp_1.html#K3" title="PSCOMP_1:func.3">|</a> <span class="p3">(<span class="default"><a href="pscomp_1.html#K17" title="PSCOMP_1:func.17">S-most</a> <font color="Maroon" title="c1">X</font></span>)</span></span>)</span> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</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> <span class="p3">(<span class="default"><a href="pscomp_1.html#K17" title="PSCOMP_1:func.17">S-most</a> <font color="Maroon" title="c1">X</font></span>)</span></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#K4" title="PSCOMP_1:func.4">proj1</a>  <a href="pscomp_1.html#K3" title="PSCOMP_1:func.3">|</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K17" title="PSCOMP_1:func.17">S-most</a> <font color="Maroon" title="c1">X</font></span>)</span></span>)</span> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</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> <span class="p2">(<span class="default"><a href="pscomp_1.html#K17" title="PSCOMP_1:func.17">S-most</a> <font color="Maroon" title="c1">X</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="measure6.html#D9" title="MEASURE6:def.9">MEASURE6:def 9</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c6">p</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E18:144"/><span class="lab"><font color="Green" title="E54">A7</font></span>: 
<font color="Maroon" title="c6">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> <span class="p2">(<span class="default"><a href="pscomp_1.html#K17" title="PSCOMP_1:func.17">S-most</a> <font color="Maroon" title="c1">X</font></span>)</span></span>)</span>
 <span class="kw">and </span><br/><a NAME="E19:144"/>
<font color="Maroon" title="c6">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> <span class="p2">(<span class="default"><a href="pscomp_1.html#K17" title="PSCOMP_1:func.17">S-most</a> <font color="Maroon" title="c1">X</font></span>)</span></span>)</span>
 <span class="kw">and </span><br/><a NAME="E20:144"/><span class="lab"><font color="Green" title="E55">A8</font></span>: 
 <a href="measure6.html#NK4" title="MEASURE6:NK.4">sup</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K4" title="PSCOMP_1:func.4">proj1</a>  <a href="pscomp_1.html#K3" title="PSCOMP_1:func.3">|</a> <span class="p3">(<span class="default"><a href="pscomp_1.html#K17" title="PSCOMP_1:func.17">S-most</a> <font color="Maroon" title="c1">X</font></span>)</span></span>)</span> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</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> <span class="p3">(<span class="default"><a href="pscomp_1.html#K17" title="PSCOMP_1:func.17">S-most</a> <font color="Maroon" title="c1">X</font></span>)</span></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#K4" title="PSCOMP_1:func.4">proj1</a>  <a href="pscomp_1.html#K3" title="PSCOMP_1:func.3">|</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K17" title="PSCOMP_1:func.17">S-most</a> <font color="Maroon" title="c1">X</font></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c6">p</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#T115" title="FUNCT_2:th.115">FUNCT_2:115</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c7">p</font> = <font color="Maroon" title="c6">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> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:144"><span class="lab"><font color="Green" title="E51">A4</font></span></a>, <a class="txt" href="#E18:144"><span class="lab"><font color="Green" title="E54">A7</font></span></a></span>;<br/>
<a NAME="E22:144"/>
<font color="Maroon" title="c7">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rltopsp1.html#K1" title="RLTOPSP1:func.1">LSeg</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K10" title="PSCOMP_1:func.10">SW-corner</a> <font color="Maroon" title="c1">X</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K13" title="PSCOMP_1:func.13">SE-corner</a> <font color="Maroon" title="c1">X</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:144"><span class="lab"><font color="Green" title="E51">A4</font></span></a>, <a class="txt" href="#E18:144"><span class="lab"><font color="Green" title="E54">A7</font></span></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></span>;<br/>
<a NAME="E23:144"/><span class="kw">then </span><span class="lab"><font color="Green" title="E56">A9</font></span>: 
<font color="Maroon" title="c7">p</font> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pscomp_1.html#K9" title="PSCOMP_1:func.9">S-bound</a> <font color="Maroon" title="c1">X</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:144"><span class="lab"><font color="Green" title="E53">A6</font></span></a>, <a class="ref" href="goboard7.html#T6" title="GOBOARD7:th.6">GOBOARD7:6</a></span>;<br/>
<a NAME="E24:144"/>
<span class="p1">(<span class="default"><a href="pscomp_1.html#K4" title="PSCOMP_1:func.4">proj1</a>  <a href="pscomp_1.html#K3" title="PSCOMP_1:func.3">|</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K17" title="PSCOMP_1:func.17">S-most</a> <font color="Maroon" title="c1">X</font></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c7">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">p</font> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:144"><span class="lab"><font color="Green" title="E51">A4</font></span></a>, <a class="txt" href="#E18:144"><span class="lab"><font color="Green" title="E54">A7</font></span></a>, <a class="ref" href="pscomp_1.html#T69" target="_self" title="PSCOMP_1:th.69">Th69</a></span>;<br/>
<span class="kw">hence </span><a NAME="E25:144"/>
 <a href="pscomp_1.html#K24" title="PSCOMP_1:func.24">S-max</a> <font color="Maroon" title="c1">X</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="pscomp_1.html#K17" title="PSCOMP_1:func.17">S-most</a> <font color="Maroon" title="c1">X</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:144"><span class="lab"><font color="Green" title="E51">A4</font></span></a>, <a class="txt" href="#E18:144"><span class="lab"><font color="Green" title="E54">A7</font></span></a>, <a class="txt" href="#E20:144"><span class="lab"><font color="Green" title="E55">A8</font></span></a>, <a class="txt" href="#E23:144"><span class="lab"><font color="Green" title="E56">A9</font></span></a>, <a class="ref" href="euclid.html#T57" title="EUCLID:th.57">EUCLID:57</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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