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

<b>let </b><font color="Maroon">X</font> be  non <a href="xboole_0.html#V1">empty</a> <a href="compts_1.html#V6">compact</a> <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="155_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:155_1_1"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3">LSeg</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K19" target="_self">SW-corner</a> <font color="Maroon">X</font></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K34" target="_self">S-min</a> <font color="Maroon">X</font></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <font color="Maroon">X</font>
 ;<br/><a NAME="E2:155_1_1"/><b>then </b><i><font color="Green">E31</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K19" target="_self">SW-corner</a> <font color="Maroon">X</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K34" target="_self">S-min</a> <font color="Maroon">X</font></span>)</span> &amp; <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> )
 <b>by </b><i><a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/><b>reconsider </b><font color="Maroon">p</font> = <font color="Maroon">x</font> as   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <b>by </b><i><a class="ref" href="pscomp_1.html#T21" target="_self">Th21</a></i>;<br/><a NAME="E4:155_1_1"/>
<span class="p1">(<span class="default"><a href="pscomp_1.html#K19" target="_self">SW-corner</a> <font color="Maroon">X</font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K34" target="_self">S-min</a> <font color="Maroon">X</font></span>)</span> <a href="euclid.html#K22">`2</a> 
 <b>by </b><i><a class="ref" href="pscomp_1.html#T17" target="_self">Th17</a></i>;<br/><a NAME="E5:155_1_1"/><b>then </b><i><font color="Green">E32</font></i>: 
<font color="Maroon">p</font> <a href="euclid.html#K22">`2</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K34" target="_self">S-min</a> <font color="Maroon">X</font></span>)</span> <a href="euclid.html#K22">`2</a> 
 <b>by </b><i><a class="ref" href="pscomp_1.html#T22" target="_self">Th22</a>, <a class="ref" href="goboard7.html#T6">GOBOARD7:6</a></i>;<br/><a NAME="E6:155_1_1"/>
<span class="p1">(<span class="default"><a href="pscomp_1.html#K19" target="_self">SW-corner</a> <font color="Maroon">X</font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K34" target="_self">S-min</a> <font color="Maroon">X</font></span>)</span> <a href="euclid.html#K21">`1</a> 
 <b>by </b><i><a class="txt" href="pscomp_1.html#E28"><i><font color="Green">Lemma107</font></i></a></i>;<br/><a NAME="E7:155_1_1"/><b>then </b><i><font color="Green">E34</font></i>: 
<font color="Maroon">p</font> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K34" target="_self">S-min</a> <font color="Maroon">X</font></span>)</span> <a href="euclid.html#K21">`1</a> 
 <b>by </b><i><a class="ref" href="pscomp_1.html#T22" target="_self">Th22</a>, <a class="ref" href="topreal1.html#T9">TOPREAL1:9</a></i>;<br/><a NAME="E8:155_1_1"/><i><font color="Green">E35</font></i>: 
 <a href="pscomp_1.html#K19" target="_self">SW-corner</a> <font color="Maroon">X</font> <a href="hidden.html#R2">in</a>  <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K19" target="_self">SW-corner</a> <font color="Maroon">X</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K22" target="_self">SE-corner</a> <font color="Maroon">X</font></span>)</span>
 <b>by </b><i><a class="ref" href="topreal1.html#T6">TOPREAL1:6</a></i>;<br/><a NAME="E9:155_1_1"/>
 <a href="pscomp_1.html#K34" target="_self">S-min</a> <font color="Maroon">X</font> <a href="hidden.html#R2">in</a>  <a href="pscomp_1.html#K26" target="_self">S-most</a> <font color="Maroon">X</font>
 <b>by </b><i><a class="ref" href="pscomp_1.html#T20" target="_self">Th20</a></i>;<br/><a NAME="E10:155_1_1"/><b>then </b>
 <a href="pscomp_1.html#K34" target="_self">S-min</a> <font color="Maroon">X</font> <a href="hidden.html#R2">in</a>  <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K19" target="_self">SW-corner</a> <font color="Maroon">X</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K22" target="_self">SE-corner</a> <font color="Maroon">X</font></span>)</span>
 <b>by </b><i><a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/><a NAME="E11:155_1_1"/><b>then </b>
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K19" target="_self">SW-corner</a> <font color="Maroon">X</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K34" target="_self">S-min</a> <font color="Maroon">X</font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K19" target="_self">SW-corner</a> <font color="Maroon">X</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K22" target="_self">SE-corner</a> <font color="Maroon">X</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="topreal1.html#T12">TOPREAL1:12</a></i>;<br/><a NAME="E12:155_1_1"/><b>then </b>
<font color="Maroon">p</font> <a href="hidden.html#R2">in</a>  <a href="pscomp_1.html#K26" target="_self">S-most</a> <font color="Maroon">X</font>
 <b>by </b><i><a class="ref" href="pscomp_1.html#T22" target="_self">Th22</a>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/><a NAME="E13:155_1_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="pscomp_1.html#K34" target="_self">S-min</a> <font color="Maroon">X</font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">p</font> <a href="euclid.html#K21">`1</a> 
 <b>by </b><i/>;<br/><a NAME="E14:155_1_1"/><b>then </b><i><font color="Green">E36</font></i>: 
<font color="Maroon">p</font> <a href="euclid.html#K21">`1</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K34" target="_self">S-min</a> <font color="Maroon">X</font></span>)</span> <a href="euclid.html#K21">`1</a> 
 <b>by </b><i><a class="txt" href="pscomp_1.html#E36"><i><font color="Green">Lemma114</font></i></a>, <a class="ref" href="xxreal_0.html#T1">XXREAL_0:1</a></i>;<br/><a NAME="E15:155_1_1"/>
<font color="Maroon">p</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="euclid.html#K23">|[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">p</font> <a href="euclid.html#K21">`1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">p</font> <a href="euclid.html#K22">`2</a> </span>)</span></span><a href="euclid.html#K23">]|</a></span>
 <b>by </b><i><a class="ref" href="euclid.html#T57">EUCLID:57</a></i>;<br/><b>hence </b><a NAME="E16:155_1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="pscomp_1.html#K34" target="_self">S-min</a> <font color="Maroon">X</font>
 <b>by </b><i><a class="txt" href="pscomp_1.html#E34"><i><font color="Green">Lemma113</font></i></a>, <a class="txt" href="pscomp_1.html#E40"><i><font color="Green">Lemma116</font></i></a>, <a class="ref" href="euclid.html#T57">EUCLID:57</a></i>;<br/></div>
<b>end;</b></div><b>assume </b><a NAME="E2:155_1"/><i><font color="Green">E40</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="pscomp_1.html#K34" target="_self">S-min</a> <font color="Maroon">X</font>
 ;<br/><a NAME="E3:155_1"/>
 <a href="pscomp_1.html#K34" target="_self">S-min</a> <font color="Maroon">X</font> <a href="hidden.html#R2">in</a>  <a href="pscomp_1.html#K26" target="_self">S-most</a> <font color="Maroon">X</font>
 <b>by </b><i><a class="ref" href="pscomp_1.html#T20" target="_self">Th20</a></i>;<br/><a NAME="E4:155_1"/><b>then </b><i><font color="Green">E41</font></i>: 
 <a href="pscomp_1.html#K34" target="_self">S-min</a> <font color="Maroon">X</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/><a NAME="E5:155_1"/>
 <a href="pscomp_1.html#K34" target="_self">S-min</a> <font color="Maroon">X</font> <a href="hidden.html#R2">in</a>  <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K19" target="_self">SW-corner</a> <font color="Maroon">X</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K34" target="_self">S-min</a> <font color="Maroon">X</font></span>)</span>
 <b>by </b><i><a class="ref" href="topreal1.html#T6">TOPREAL1:6</a></i>;<br/><b>hence </b><a NAME="E6:155_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3">LSeg</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K19" target="_self">SW-corner</a> <font color="Maroon">X</font></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K34" target="_self">S-min</a> <font color="Maroon">X</font></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <font color="Maroon">X</font>
 <b>by </b><i><a class="ref" href="pscomp_1.html#T21" target="_self">Th21</a>, <a class="ref" href="pscomp_1.html#T22" target="_self">Th22</a>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:155"/>
<span class="p1">(<span class="default"><a href="topreal1.html#K3">LSeg</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K19" target="_self">SW-corner</a> <font color="Maroon">X</font></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K34" target="_self">S-min</a> <font color="Maroon">X</font></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <font color="Maroon">X</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K34" target="_self">S-min</a> <font color="Maroon">X</font></span>)</span></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="155_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:155_2_1"/><i><font color="Green">E43</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3">LSeg</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K33" target="_self">S-max</a> <font color="Maroon">X</font></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K22" target="_self">SE-corner</a> <font color="Maroon">X</font></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <font color="Maroon">X</font>
 ;<br/><a NAME="E2:155_2_1"/><b>then </b><i><font color="Green">E44</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K33" target="_self">S-max</a> <font color="Maroon">X</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K22" target="_self">SE-corner</a> <font color="Maroon">X</font></span>)</span> &amp; <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> )
 <b>by </b><i><a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/><b>reconsider </b><font color="Maroon">p</font> = <font color="Maroon">x</font> as   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <b>by </b><i><a class="ref" href="pscomp_1.html#T21" target="_self">Th21</a></i>;<br/><a NAME="E4:155_2_1"/>
<span class="p1">(<span class="default"><a href="pscomp_1.html#K22" target="_self">SE-corner</a> <font color="Maroon">X</font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K33" target="_self">S-max</a> <font color="Maroon">X</font></span>)</span> <a href="euclid.html#K22">`2</a> 
 <b>by </b><i><a class="ref" href="pscomp_1.html#T17" target="_self">Th17</a></i>;<br/><a NAME="E5:155_2_1"/><b>then </b><i><font color="Green">E45</font></i>: 
<font color="Maroon">p</font> <a href="euclid.html#K22">`2</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K33" target="_self">S-max</a> <font color="Maroon">X</font></span>)</span> <a href="euclid.html#K22">`2</a> 
 <b>by </b><i><a class="ref" href="pscomp_1.html#T22" target="_self">Th22</a>, <a class="ref" href="goboard7.html#T6">GOBOARD7:6</a></i>;<br/><a NAME="E6:155_2_1"/>
<span class="p1">(<span class="default"><a href="pscomp_1.html#K33" target="_self">S-max</a> <font color="Maroon">X</font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K22" target="_self">SE-corner</a> <font color="Maroon">X</font></span>)</span> <a href="euclid.html#K21">`1</a> 
 <b>by </b><i><a class="txt" href="pscomp_1.html#E28"><i><font color="Green">Lemma107</font></i></a></i>;<br/><a NAME="E7:155_2_1"/><b>then </b><i><font color="Green">E46</font></i>: 
<span class="p1">(<span class="default"><a href="pscomp_1.html#K33" target="_self">S-max</a> <font color="Maroon">X</font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">p</font> <a href="euclid.html#K21">`1</a> 
 <b>by </b><i><a class="ref" href="pscomp_1.html#T22" target="_self">Th22</a>, <a class="ref" href="topreal1.html#T9">TOPREAL1:9</a></i>;<br/><a NAME="E8:155_2_1"/><i><font color="Green">E49</font></i>: 
 <a href="pscomp_1.html#K22" target="_self">SE-corner</a> <font color="Maroon">X</font> <a href="hidden.html#R2">in</a>  <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K19" target="_self">SW-corner</a> <font color="Maroon">X</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K22" target="_self">SE-corner</a> <font color="Maroon">X</font></span>)</span>
 <b>by </b><i><a class="ref" href="topreal1.html#T6">TOPREAL1:6</a></i>;<br/><a NAME="E9:155_2_1"/>
 <a href="pscomp_1.html#K33" target="_self">S-max</a> <font color="Maroon">X</font> <a href="hidden.html#R2">in</a>  <a href="pscomp_1.html#K26" target="_self">S-most</a> <font color="Maroon">X</font>
 <b>by </b><i><a class="ref" href="pscomp_1.html#T20" target="_self">Th20</a></i>;<br/><a NAME="E10:155_2_1"/><b>then </b>
 <a href="pscomp_1.html#K33" target="_self">S-max</a> <font color="Maroon">X</font> <a href="hidden.html#R2">in</a>  <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K19" target="_self">SW-corner</a> <font color="Maroon">X</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K22" target="_self">SE-corner</a> <font color="Maroon">X</font></span>)</span>
 <b>by </b><i><a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/><a NAME="E11:155_2_1"/><b>then </b>
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K33" target="_self">S-max</a> <font color="Maroon">X</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K22" target="_self">SE-corner</a> <font color="Maroon">X</font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K19" target="_self">SW-corner</a> <font color="Maroon">X</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K22" target="_self">SE-corner</a> <font color="Maroon">X</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="topreal1.html#T12">TOPREAL1:12</a></i>;<br/><a NAME="E12:155_2_1"/><b>then </b>
<font color="Maroon">p</font> <a href="hidden.html#R2">in</a>  <a href="pscomp_1.html#K26" target="_self">S-most</a> <font color="Maroon">X</font>
 <b>by </b><i><a class="ref" href="pscomp_1.html#T22" target="_self">Th22</a>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/><a NAME="E13:155_2_1"/><b>then </b>
<font color="Maroon">p</font> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K33" target="_self">S-max</a> <font color="Maroon">X</font></span>)</span> <a href="euclid.html#K21">`1</a> 
 <b>by </b><i/>;<br/><a NAME="E14:155_2_1"/><b>then </b><i><font color="Green">E50</font></i>: 
<font color="Maroon">p</font> <a href="euclid.html#K21">`1</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K33" target="_self">S-max</a> <font color="Maroon">X</font></span>)</span> <a href="euclid.html#K21">`1</a> 
 <b>by </b><i><a class="txt" href="pscomp_1.html#E36"><i><font color="Green">Lemma114</font></i></a>, <a class="ref" href="xxreal_0.html#T1">XXREAL_0:1</a></i>;<br/><a NAME="E15:155_2_1"/>
<font color="Maroon">p</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="euclid.html#K23">|[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">p</font> <a href="euclid.html#K21">`1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">p</font> <a href="euclid.html#K22">`2</a> </span>)</span></span><a href="euclid.html#K23">]|</a></span>
 <b>by </b><i><a class="ref" href="euclid.html#T57">EUCLID:57</a></i>;<br/><b>hence </b><a NAME="E16:155_2_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="pscomp_1.html#K33" target="_self">S-max</a> <font color="Maroon">X</font>
 <b>by </b><i><a class="txt" href="pscomp_1.html#E34"><i><font color="Green">Lemma113</font></i></a>, <a class="txt" href="pscomp_1.html#E40"><i><font color="Green">Lemma116</font></i></a>, <a class="ref" href="euclid.html#T57">EUCLID:57</a></i>;<br/></div>
<b>end;</b></div><b>assume </b><a NAME="E2:155_2"/><i><font color="Green">E51</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="pscomp_1.html#K33" target="_self">S-max</a> <font color="Maroon">X</font>
 ;<br/><a NAME="E3:155_2"/>
 <a href="pscomp_1.html#K33" target="_self">S-max</a> <font color="Maroon">X</font> <a href="hidden.html#R2">in</a>  <a href="pscomp_1.html#K26" target="_self">S-most</a> <font color="Maroon">X</font>
 <b>by </b><i><a class="ref" href="pscomp_1.html#T20" target="_self">Th20</a></i>;<br/><a NAME="E4:155_2"/><b>then </b><i><font color="Green">E52</font></i>: 
 <a href="pscomp_1.html#K33" target="_self">S-max</a> <font color="Maroon">X</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/><a NAME="E5:155_2"/>
 <a href="pscomp_1.html#K33" target="_self">S-max</a> <font color="Maroon">X</font> <a href="hidden.html#R2">in</a>  <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K33" target="_self">S-max</a> <font color="Maroon">X</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K22" target="_self">SE-corner</a> <font color="Maroon">X</font></span>)</span>
 <b>by </b><i><a class="ref" href="topreal1.html#T6">TOPREAL1:6</a></i>;<br/><b>hence </b><a NAME="E6:155_2"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3">LSeg</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K33" target="_self">S-max</a> <font color="Maroon">X</font></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K22" target="_self">SE-corner</a> <font color="Maroon">X</font></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <font color="Maroon">X</font>
 <b>by </b><i><a class="ref" href="pscomp_1.html#T21" target="_self">Th21</a>, <a class="ref" href="pscomp_1.html#T22" target="_self">Th22</a>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:155"/>
<span class="p1">(<span class="default"><a href="topreal1.html#K3">LSeg</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K33" target="_self">S-max</a> <font color="Maroon">X</font></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K22" target="_self">SE-corner</a> <font color="Maroon">X</font></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <font color="Maroon">X</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K33" target="_self">S-max</a> <font color="Maroon">X</font></span>)</span></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>


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