<?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="131_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="E1:131_1_1"/><i><font color="Green">E94</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#K19" target="_self">SW-corner</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K27" target="_self">W-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="E2:131_1_1"/><b>then </b><i><font color="Green">E95</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#K19" target="_self">SW-corner</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K27" target="_self">W-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#E1:131_1_1"><i><font color="Green">E94</font></i></a></i>;<br/><a NAME="E4:131_1_1"/>
<span class="p1">(<span class="default"><a href="pscomp_1.html#K19" target="_self">SW-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#K27" target="_self">W-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#T85" target="_self">Th85</a></i>;<br/><a NAME="E5:131_1_1"/><b>then </b><i><font color="Green">E96</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#K27" target="_self">W-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#E2:131_1_1"><i><font color="Green">E95</font></i></a>, <a class="ref" href="goboard7.html#T5">GOBOARD7:5</a></i>;<br/><a NAME="E6:131_1_1"/>
<span class="p1">(<span class="default"><a href="pscomp_1.html#K19" target="_self">SW-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#K27" target="_self">W-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#T87" target="_self">Th87</a></i>;<br/><a NAME="E7:131_1_1"/><b>then </b><i><font color="Green">E97</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#K27" target="_self">W-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#E2:131_1_1"><i><font color="Green">E95</font></i></a>, <a class="ref" href="topreal1.html#T10">TOPREAL1:10</a></i>;<br/><a NAME="E8:131_1_1"/><i><font color="Green">E98</font></i>: 
 <a href="pscomp_1.html#K19" target="_self">SW-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#K19" target="_self">SW-corner</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K20" target="_self">NW-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="E9:131_1_1"/>
 <a href="pscomp_1.html#K27" target="_self">W-min</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="pscomp_1.html#K23" target="_self">W-most</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="pscomp_1.html#T91" target="_self">Th91</a></i>;<br/><a NAME="E10:131_1_1"/><b>then </b>
 <a href="pscomp_1.html#K27" target="_self">W-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#K19" target="_self">SW-corner</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K20" target="_self">NW-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="E11:131_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">c<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K27" target="_self">W-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#K19" target="_self">SW-corner</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K20" target="_self">NW-corner</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="pscomp_1.html#E8:131_1_1"><i><font color="Green">E98</font></i></a>, <a class="ref" href="topreal1.html#T12">TOPREAL1:12</a></i>;<br/><a NAME="E12:131_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#K23" target="_self">W-most</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="pscomp_1.html#E2:131_1_1"><i><font color="Green">E95</font></i></a>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/><a NAME="E13:131_1_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="pscomp_1.html#K27" target="_self">W-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#T88" target="_self">Th88</a></i>;<br/><a NAME="E14:131_1_1"/><b>then </b><i><font color="Green">E99</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#K27" target="_self">W-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#E7:131_1_1"><i><font color="Green">E97</font></i></a>, <a class="ref" href="xxreal_0.html#T1">XXREAL_0:1</a></i>;<br/><a NAME="E15:131_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="E16:131_1_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="pscomp_1.html#K27" target="_self">W-min</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="pscomp_1.html#E5:131_1_1"><i><font color="Green">E96</font></i></a>, <a class="txt" href="pscomp_1.html#E14:131_1_1"><i><font color="Green">E99</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="E2:131_1"/><i><font color="Green">E94</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="pscomp_1.html#K27" target="_self">W-min</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/><a NAME="E3:131_1"/>
 <a href="pscomp_1.html#K27" target="_self">W-min</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="pscomp_1.html#K23" target="_self">W-most</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="pscomp_1.html#T91" target="_self">Th91</a></i>;<br/><a NAME="E4:131_1"/><b>then </b><i><font color="Green">E95</font></i>: 
 <a href="pscomp_1.html#K27" target="_self">W-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="E5:131_1"/>
 <a href="pscomp_1.html#K27" target="_self">W-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#K19" target="_self">SW-corner</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K27" target="_self">W-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="E6:131_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#K19" target="_self">SW-corner</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K27" target="_self">W-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#E2:131_1"><i><font color="Green">E94</font></i></a>, <a class="txt" href="pscomp_1.html#E4:131_1"><i><font color="Green">E95</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="E2:131"/>
<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">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K27" target="_self">W-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#K27" target="_self">W-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="131_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="E1:131_2_1"/><i><font color="Green">E94</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#K28" target="_self">W-max</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K20" target="_self">NW-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="E2:131_2_1"/><b>then </b><i><font color="Green">E95</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#K28" target="_self">W-max</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K20" target="_self">NW-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#E1:131_2_1"><i><font color="Green">E94</font></i></a></i>;<br/><a NAME="E4:131_2_1"/>
<span class="p1">(<span class="default"><a href="pscomp_1.html#K20" target="_self">NW-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#K28" target="_self">W-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#T85" target="_self">Th85</a></i>;<br/><a NAME="E5:131_2_1"/><b>then </b><i><font color="Green">E96</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#K28" target="_self">W-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#E2:131_2_1"><i><font color="Green">E95</font></i></a>, <a class="ref" href="goboard7.html#T5">GOBOARD7:5</a></i>;<br/><a NAME="E6:131_2_1"/>
<span class="p1">(<span class="default"><a href="pscomp_1.html#K28" target="_self">W-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#K20" target="_self">NW-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#T87" target="_self">Th87</a></i>;<br/><a NAME="E7:131_2_1"/><b>then </b><i><font color="Green">E97</font></i>: 
<span class="p1">(<span class="default"><a href="pscomp_1.html#K28" target="_self">W-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#E2:131_2_1"><i><font color="Green">E95</font></i></a>, <a class="ref" href="topreal1.html#T10">TOPREAL1:10</a></i>;<br/><a NAME="E8:131_2_1"/><i><font color="Green">E98</font></i>: 
 <a href="pscomp_1.html#K20" target="_self">NW-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#K19" target="_self">SW-corner</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K20" target="_self">NW-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="E9:131_2_1"/>
 <a href="pscomp_1.html#K28" target="_self">W-max</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="pscomp_1.html#K23" target="_self">W-most</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="pscomp_1.html#T91" target="_self">Th91</a></i>;<br/><a NAME="E10:131_2_1"/><b>then </b>
 <a href="pscomp_1.html#K28" target="_self">W-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#K19" target="_self">SW-corner</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K20" target="_self">NW-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="E11:131_2_1"/><b>then </b>
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K28" target="_self">W-max</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K20" target="_self">NW-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#K19" target="_self">SW-corner</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K20" target="_self">NW-corner</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="pscomp_1.html#E8:131_2_1"><i><font color="Green">E98</font></i></a>, <a class="ref" href="topreal1.html#T12">TOPREAL1:12</a></i>;<br/><a NAME="E12:131_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#K23" target="_self">W-most</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="pscomp_1.html#E2:131_2_1"><i><font color="Green">E95</font></i></a>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/><a NAME="E13:131_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#K28" target="_self">W-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#T88" target="_self">Th88</a></i>;<br/><a NAME="E14:131_2_1"/><b>then </b><i><font color="Green">E99</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#K28" target="_self">W-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#E7:131_2_1"><i><font color="Green">E97</font></i></a>, <a class="ref" href="xxreal_0.html#T1">XXREAL_0:1</a></i>;<br/><a NAME="E15:131_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="E16:131_2_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="pscomp_1.html#K28" target="_self">W-max</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="pscomp_1.html#E5:131_2_1"><i><font color="Green">E96</font></i></a>, <a class="txt" href="pscomp_1.html#E14:131_2_1"><i><font color="Green">E99</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="E2:131_2"/><i><font color="Green">E94</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="pscomp_1.html#K28" target="_self">W-max</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/><a NAME="E3:131_2"/>
 <a href="pscomp_1.html#K28" target="_self">W-max</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="pscomp_1.html#K23" target="_self">W-most</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="pscomp_1.html#T91" target="_self">Th91</a></i>;<br/><a NAME="E4:131_2"/><b>then </b><i><font color="Green">E95</font></i>: 
 <a href="pscomp_1.html#K28" target="_self">W-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="E5:131_2"/>
 <a href="pscomp_1.html#K28" target="_self">W-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#K28" target="_self">W-max</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K20" target="_self">NW-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="E6:131_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#K28" target="_self">W-max</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K20" target="_self">NW-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#E2:131_2"><i><font color="Green">E94</font></i></a>, <a class="txt" href="pscomp_1.html#E4:131_2"><i><font color="Green">E95</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="E4:131"/>
<span class="p1">(<span class="default"><a href="topreal1.html#K3">LSeg</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K28" target="_self">W-max</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K20" target="_self">NW-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#K28" target="_self">W-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>
