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

<b>let </b><font color="Maroon">c<sub>1</sub></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="147_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:147_1_1"/><i><font color="Green">E108</font></i>: 
<font color="Maroon">c<sub>2</sub></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#K22" target="_self">SE-corner</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K32" target="_self">E-min</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/><a NAME="E2:147_1_1"/><b>then </b><i><font color="Green">E109</font></i>: 
( <font color="Maroon">c<sub>2</sub></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#K22" target="_self">SE-corner</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K32" target="_self">E-min</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></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">c<sub>3</sub></font> = <font color="Maroon">c<sub>2</sub></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="txt" href="pscomp_1.html#E1:147_1_1"><i><font color="Green">E108</font></i></a></i>;<br/><a NAME="E4:147_1_1"/>
<span class="p1">(<span class="default"><a href="pscomp_1.html#K22" target="_self">SE-corner</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K32" target="_self">E-min</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> 
 <b>by </b><i><a class="ref" href="pscomp_1.html#T105" target="_self">Th105</a></i>;<br/><a NAME="E5:147_1_1"/><b>then </b><i><font color="Green">E110</font></i>: 
<font color="Maroon">c<sub>3</sub></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#K32" target="_self">E-min</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> 
 <b>by </b><i><a class="txt" href="pscomp_1.html#E2:147_1_1"><i><font color="Green">E109</font></i></a>, <a class="ref" href="goboard7.html#T5">GOBOARD7:5</a></i>;<br/><a NAME="E6:147_1_1"/>
<span class="p1">(<span class="default"><a href="pscomp_1.html#K22" target="_self">SE-corner</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K32" target="_self">E-min</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> 
 <b>by </b><i><a class="ref" href="pscomp_1.html#T107" target="_self">Th107</a></i>;<br/><a NAME="E7:147_1_1"/><b>then </b><i><font color="Green">E111</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K32" target="_self">E-min</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> 
 <b>by </b><i><a class="txt" href="pscomp_1.html#E2:147_1_1"><i><font color="Green">E109</font></i></a>, <a class="ref" href="topreal1.html#T10">TOPREAL1:10</a></i>;<br/><a NAME="E8:147_1_1"/><i><font color="Green">E112</font></i>: 
 <a href="pscomp_1.html#K22" target="_self">SE-corner</a> <font color="Maroon">c<sub>1</sub></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#K22" target="_self">SE-corner</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K21" target="_self">NE-corner</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="topreal1.html#T6">TOPREAL1:6</a></i>;<br/><a NAME="E9:147_1_1"/>
 <a href="pscomp_1.html#K32" target="_self">E-min</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="pscomp_1.html#K25" target="_self">E-most</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="pscomp_1.html#T111" target="_self">Th111</a></i>;<br/><a NAME="E10:147_1_1"/><b>then </b>
 <a href="pscomp_1.html#K32" target="_self">E-min</a> <font color="Maroon">c<sub>1</sub></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#K22" target="_self">SE-corner</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K21" target="_self">NE-corner</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/><a NAME="E11:147_1_1"/><b>then </b>
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K22" target="_self">SE-corner</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K32" target="_self">E-min</a> <font color="Maroon">c<sub>1</sub></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#K22" target="_self">SE-corner</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K21" target="_self">NE-corner</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="pscomp_1.html#E8:147_1_1"><i><font color="Green">E112</font></i></a>, <a class="ref" href="topreal1.html#T12">TOPREAL1:12</a></i>;<br/><a NAME="E12:147_1_1"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="pscomp_1.html#K25" target="_self">E-most</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="pscomp_1.html#E2:147_1_1"><i><font color="Green">E109</font></i></a>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/><a NAME="E13:147_1_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="pscomp_1.html#K32" target="_self">E-min</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>3</sub></font> <a href="euclid.html#K22">`2</a> 
 <b>by </b><i><a class="ref" href="pscomp_1.html#T108" target="_self">Th108</a></i>;<br/><a NAME="E14:147_1_1"/><b>then </b><i><font color="Green">E113</font></i>: 
<font color="Maroon">c<sub>3</sub></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#K32" target="_self">E-min</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> 
 <b>by </b><i><a class="txt" href="pscomp_1.html#E7:147_1_1"><i><font color="Green">E111</font></i></a>, <a class="ref" href="xxreal_0.html#T1">XXREAL_0:1</a></i>;<br/><a NAME="E15:147_1_1"/>
<font color="Maroon">c<sub>3</sub></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">c<sub>3</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></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="E16:147_1_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="pscomp_1.html#K32" target="_self">E-min</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="pscomp_1.html#E5:147_1_1"><i><font color="Green">E110</font></i></a>, <a class="txt" href="pscomp_1.html#E14:147_1_1"><i><font color="Green">E113</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="E2:147_1"/><i><font color="Green">E108</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="pscomp_1.html#K32" target="_self">E-min</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/><a NAME="E3:147_1"/>
 <a href="pscomp_1.html#K32" target="_self">E-min</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="pscomp_1.html#K25" target="_self">E-most</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="pscomp_1.html#T111" target="_self">Th111</a></i>;<br/><a NAME="E4:147_1"/><b>then </b><i><font color="Green">E109</font></i>: 
 <a href="pscomp_1.html#K32" target="_self">E-min</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/><a NAME="E5:147_1"/>
 <a href="pscomp_1.html#K32" target="_self">E-min</a> <font color="Maroon">c<sub>1</sub></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#K22" target="_self">SE-corner</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K32" target="_self">E-min</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="topreal1.html#T6">TOPREAL1:6</a></i>;<br/><b>hence </b><a NAME="E6:147_1"/>
<font color="Maroon">c<sub>2</sub></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#K22" target="_self">SE-corner</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K32" target="_self">E-min</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="pscomp_1.html#E2:147_1"><i><font color="Green">E108</font></i></a>, <a class="txt" href="pscomp_1.html#E4:147_1"><i><font color="Green">E109</font></i></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="E2:147"/>
<span class="p1">(<span class="default"><a href="topreal1.html#K3">LSeg</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K22" target="_self">SE-corner</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K32" target="_self">E-min</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <font color="Maroon">c<sub>1</sub></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#K32" target="_self">E-min</a> <font color="Maroon">c<sub>1</sub></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="147_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:147_2_1"/><i><font color="Green">E108</font></i>: 
<font color="Maroon">c<sub>2</sub></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#K31" target="_self">E-max</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K21" target="_self">NE-corner</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/><a NAME="E2:147_2_1"/><b>then </b><i><font color="Green">E109</font></i>: 
( <font color="Maroon">c<sub>2</sub></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#K31" target="_self">E-max</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K21" target="_self">NE-corner</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></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">c<sub>3</sub></font> = <font color="Maroon">c<sub>2</sub></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="txt" href="pscomp_1.html#E1:147_2_1"><i><font color="Green">E108</font></i></a></i>;<br/><a NAME="E4:147_2_1"/>
<span class="p1">(<span class="default"><a href="pscomp_1.html#K21" target="_self">NE-corner</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K31" target="_self">E-max</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> 
 <b>by </b><i><a class="ref" href="pscomp_1.html#T105" target="_self">Th105</a></i>;<br/><a NAME="E5:147_2_1"/><b>then </b><i><font color="Green">E110</font></i>: 
<font color="Maroon">c<sub>3</sub></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#K31" target="_self">E-max</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="euclid.html#K21">`1</a> 
 <b>by </b><i><a class="txt" href="pscomp_1.html#E2:147_2_1"><i><font color="Green">E109</font></i></a>, <a class="ref" href="goboard7.html#T5">GOBOARD7:5</a></i>;<br/><a NAME="E6:147_2_1"/>
<span class="p1">(<span class="default"><a href="pscomp_1.html#K31" target="_self">E-max</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K21" target="_self">NE-corner</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> 
 <b>by </b><i><a class="ref" href="pscomp_1.html#T107" target="_self">Th107</a></i>;<br/><a NAME="E7:147_2_1"/><b>then </b><i><font color="Green">E111</font></i>: 
<span class="p1">(<span class="default"><a href="pscomp_1.html#K31" target="_self">E-max</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>3</sub></font> <a href="euclid.html#K22">`2</a> 
 <b>by </b><i><a class="txt" href="pscomp_1.html#E2:147_2_1"><i><font color="Green">E109</font></i></a>, <a class="ref" href="topreal1.html#T10">TOPREAL1:10</a></i>;<br/><a NAME="E8:147_2_1"/><i><font color="Green">E112</font></i>: 
 <a href="pscomp_1.html#K21" target="_self">NE-corner</a> <font color="Maroon">c<sub>1</sub></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#K22" target="_self">SE-corner</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K21" target="_self">NE-corner</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="topreal1.html#T6">TOPREAL1:6</a></i>;<br/><a NAME="E9:147_2_1"/>
 <a href="pscomp_1.html#K31" target="_self">E-max</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="pscomp_1.html#K25" target="_self">E-most</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="pscomp_1.html#T111" target="_self">Th111</a></i>;<br/><a NAME="E10:147_2_1"/><b>then </b>
 <a href="pscomp_1.html#K31" target="_self">E-max</a> <font color="Maroon">c<sub>1</sub></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#K22" target="_self">SE-corner</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K21" target="_self">NE-corner</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/><a NAME="E11:147_2_1"/><b>then </b>
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K31" target="_self">E-max</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K21" target="_self">NE-corner</a> <font color="Maroon">c<sub>1</sub></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#K22" target="_self">SE-corner</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K21" target="_self">NE-corner</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="pscomp_1.html#E8:147_2_1"><i><font color="Green">E112</font></i></a>, <a class="ref" href="topreal1.html#T12">TOPREAL1:12</a></i>;<br/><a NAME="E12:147_2_1"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="pscomp_1.html#K25" target="_self">E-most</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="pscomp_1.html#E2:147_2_1"><i><font color="Green">E109</font></i></a>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/><a NAME="E13:147_2_1"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K31" target="_self">E-max</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> 
 <b>by </b><i><a class="ref" href="pscomp_1.html#T108" target="_self">Th108</a></i>;<br/><a NAME="E14:147_2_1"/><b>then </b><i><font color="Green">E113</font></i>: 
<font color="Maroon">c<sub>3</sub></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#K31" target="_self">E-max</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> 
 <b>by </b><i><a class="txt" href="pscomp_1.html#E7:147_2_1"><i><font color="Green">E111</font></i></a>, <a class="ref" href="xxreal_0.html#T1">XXREAL_0:1</a></i>;<br/><a NAME="E15:147_2_1"/>
<font color="Maroon">c<sub>3</sub></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">c<sub>3</sub></font> <a href="euclid.html#K21">`1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></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="E16:147_2_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="pscomp_1.html#K31" target="_self">E-max</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="pscomp_1.html#E5:147_2_1"><i><font color="Green">E110</font></i></a>, <a class="txt" href="pscomp_1.html#E14:147_2_1"><i><font color="Green">E113</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="E2:147_2"/><i><font color="Green">E108</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="pscomp_1.html#K31" target="_self">E-max</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/><a NAME="E3:147_2"/>
 <a href="pscomp_1.html#K31" target="_self">E-max</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="pscomp_1.html#K25" target="_self">E-most</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="pscomp_1.html#T111" target="_self">Th111</a></i>;<br/><a NAME="E4:147_2"/><b>then </b><i><font color="Green">E109</font></i>: 
 <a href="pscomp_1.html#K31" target="_self">E-max</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/><a NAME="E5:147_2"/>
 <a href="pscomp_1.html#K31" target="_self">E-max</a> <font color="Maroon">c<sub>1</sub></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#K31" target="_self">E-max</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K21" target="_self">NE-corner</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="topreal1.html#T6">TOPREAL1:6</a></i>;<br/><b>hence </b><a NAME="E6:147_2"/>
<font color="Maroon">c<sub>2</sub></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#K31" target="_self">E-max</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K21" target="_self">NE-corner</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="pscomp_1.html#E2:147_2"><i><font color="Green">E108</font></i></a>, <a class="txt" href="pscomp_1.html#E4:147_2"><i><font color="Green">E109</font></i></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="E4:147"/>
<span class="p1">(<span class="default"><a href="topreal1.html#K3">LSeg</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K31" target="_self">E-max</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K21" target="_self">NE-corner</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <font color="Maroon">c<sub>1</sub></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#K31" target="_self">E-max</a> <font color="Maroon">c<sub>1</sub></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>
