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

<b>let </b><font color="Maroon">FT</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="orders_2.html#L1">RelStr</a> ;<br/><b>let </b><font color="Maroon">A</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">FT</font>, <font color="Maroon">C</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">FT</font>;<br/>



<b>assume </b><b>that </b><br/><a NAME="E1:46"/><i><font color="Green">E27</font></i>: 
<font color="Maroon">FT</font> is <a href="fin_topo.html#V2">symmetric</a>
 <b>and </b><br/><a NAME="E2:46"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">C</font> is <a href="fin_topo.html#V5">connected</a>
 <b>and </b><br/><a NAME="E3:46"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">C</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">A</font>
 <b>and </b><br/><a NAME="E4:46"/><i><font color="Green">E41</font></i>: 
<font color="Maroon">A</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">C</font> <a href="fin_topo.html#K9">^b</a> 
 ;<br/>

<b>let </b><font color="Maroon">P2</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">FT</font>, <font color="Maroon">Q2</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">FT</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="fin_topo.html#D18">FIN_TOPO:def 18</a><br/>

<b>assume </b><a NAME="E5:46"/><i><font color="Green">E43</font></i>: 
( <font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <font color="Maroon">P2</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">Q2</font> &amp; <font color="Maroon">P2</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <font color="Maroon">Q2</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <font color="Maroon">P2</font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">Q2</font> )
 ;<br/>

<b>assume </b><a NAME="E6:46"/><i><font color="Green">E57</font></i>: 
<font color="Maroon">P2</font> <a href="fin_topo.html#K9">^b</a>  <a href="xboole_0.html#R1">misses</a> <font color="Maroon">Q2</font>
 ;<br/>

<a NAME="E7:46"/>
<font color="Maroon">P2</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">P2</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">Q2</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a></i>;<br/>
<a NAME="E8:46"/><b>then </b><i><font color="Green">E60</font></i>: 
<font color="Maroon">P2</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">C</font> <a href="fin_topo.html#K9">^b</a> 
 
<b>by </b><i><a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a>, , <a class="ref" href="fintopo6.html#T1" target="_self">Th1</a></i>;<br/>
<b>consider </b><font color="Maroon">x</font> being    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">P2</font>;<br/>
<a NAME="E10:46"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">P2</font>
 
<b>by </b><i/>;<br/>
<a NAME="E11:46"/><b>then </b>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font> <a href="fin_topo.html#K9">^b</a> 
 
<b>by </b><i><a class="txt" href="fintopo6.html#E2:46"><i><font color="Green">E31</font></i></a></i>;<br/>
<b>then consider </b><font color="Maroon">z</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">FT</font><b> such that </b><br/><a NAME="E13:46"/><i><font color="Green">E71</font></i>: 
( <font color="Maroon">z</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> &amp;  <a href="fin_topo.html#K1">U_FT</a> <font color="Maroon">z</font> <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Maroon">C</font> )
 ;<br/>
<a NAME="E14:46"/><i><font color="Green">E81</font></i>: 
<span class="p1">(<span class="default"><a href="fin_topo.html#K1">U_FT</a> <font color="Maroon">z</font></span>)</span> <a href="subset_1.html#K9">/\</a> <font color="Maroon">C</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i>, <a class="ref" href="xboole_0.html#D7">XBOOLE_0:def 7</a></i>;<br/>
<b>consider </b><font color="Maroon">y</font> being    <a href="subset_1.html#M1">Element</a> of <span class="p1">(<span class="default"><a href="fin_topo.html#K1">U_FT</a> <font color="Maroon">z</font></span>)</span> <a href="subset_1.html#K9">/\</a> <font color="Maroon">C</font>;<br/>
<a NAME="E16:46"/><i><font color="Green">E82</font></i>: 
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="fin_topo.html#K1">U_FT</a> <font color="Maroon">z</font></span>)</span> <a href="subset_1.html#K9">/\</a> <font color="Maroon">C</font>
 
<b>by </b><i><a class="txt" href="fintopo6.html#E3:46"><i><font color="Green">E33</font></i></a></i>;<br/>
<a NAME="E17:46"/><i><font color="Green">E83</font></i>: 
( <font color="Maroon">y</font> <a href="hidden.html#R2">in</a>  <a href="fin_topo.html#K1">U_FT</a> <font color="Maroon">z</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font> )
 
<b>by </b><i><a class="txt" href="fintopo6.html#E3:46"><i><font color="Green">E33</font></i></a>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<b>reconsider </b><font color="Maroon">y2</font> = <font color="Maroon">y</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">FT</font> <b>by </b><i><a class="ref" href="fintopo6.html#T2" target="_self">Th2</a></i>;<br/>
<a NAME="E19:46"/>
<font color="Maroon">z</font> <a href="hidden.html#R2">in</a>  <a href="fin_topo.html#K1">U_FT</a> <font color="Maroon">y2</font>
 
<b>by </b><i><a class="ref" href="fintopo6.html#T3" target="_self">Th3</a>, <a class="ref" href="fin_topo.html#D15">FIN_TOPO:def 15</a>, </i>;<br/>
<a NAME="E20:46"/><b>then </b>
<font color="Maroon">z</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="fin_topo.html#K1">U_FT</a> <font color="Maroon">y2</font></span>)</span> <a href="subset_1.html#K9">/\</a> <font color="Maroon">P2</font>
 
<b>by </b><i>, , <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<a NAME="E21:46"/><b>then </b>
 <a href="fin_topo.html#K1">U_FT</a> <font color="Maroon">y2</font> <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Maroon">P2</font>
 
<b>by </b><i><a class="ref" href="xboole_0.html#D7">XBOOLE_0:def 7</a></i>;<br/>
<a NAME="E22:46"/><b>then </b><i><font color="Green">E84</font></i>: 
<font color="Maroon">y2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">P2</font> <a href="fin_topo.html#K9">^b</a> 
 
;<br/>
<a NAME="E23:46"/><i><font color="Green">E85</font></i>: 
<font color="Maroon">y2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font>
 
<b>by </b><i><a class="txt" href="fintopo6.html#E3:46"><i><font color="Green">E33</font></i></a>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<a NAME="E24:46"/>
<font color="Maroon">Q2</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">Q2</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">P2</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a></i>;<br/>
<a NAME="E25:46"/><b>then </b><i><font color="Green">E86</font></i>: 
<font color="Maroon">Q2</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">C</font> <a href="fin_topo.html#K9">^b</a> 
 
<b>by </b><i>, <a class="ref" href="fintopo6.html#T1" target="_self">Th1</a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<b>consider </b><font color="Maroon">x2</font> being    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">Q2</font>;<br/>
<a NAME="E27:46"/>
<font color="Maroon">x2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Q2</font>
 
<b>by </b><i/>;<br/>
<a NAME="E28:46"/><b>then </b>
<font color="Maroon">x2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font> <a href="fin_topo.html#K9">^b</a> 
 
<b>by </b><i/>;<br/>
<b>then consider </b><font color="Maroon">z2</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">FT</font><b> such that </b><br/><a NAME="E30:46"/><i><font color="Green">E87</font></i>: 
( <font color="Maroon">z2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x2</font> &amp;  <a href="fin_topo.html#K1">U_FT</a> <font color="Maroon">z2</font> <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Maroon">C</font> )
 ;<br/>
<a NAME="E31:46"/><i><font color="Green">E97</font></i>: 
<span class="p1">(<span class="default"><a href="fin_topo.html#K1">U_FT</a> <font color="Maroon">z2</font></span>)</span> <a href="subset_1.html#K9">/\</a> <font color="Maroon">C</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="ref" href="fintopo6.html#T5" target="_self">Th5</a>, <a class="ref" href="xboole_0.html#D7">XBOOLE_0:def 7</a></i>;<br/>
<b>consider </b><font color="Maroon">y3</font> being    <a href="subset_1.html#M1">Element</a> of <span class="p1">(<span class="default"><a href="fin_topo.html#K1">U_FT</a> <font color="Maroon">z2</font></span>)</span> <a href="subset_1.html#K9">/\</a> <font color="Maroon">C</font>;<br/>
<a NAME="E33:46"/><i><font color="Green">E98</font></i>: 
<font color="Maroon">y3</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="fin_topo.html#K1">U_FT</a> <font color="Maroon">z2</font></span>)</span> <a href="subset_1.html#K9">/\</a> <font color="Maroon">C</font>
 
<b>by </b><i><a class="ref" href="fintopo6.html#T6" target="_self">Th6</a></i>;<br/>
<a NAME="E34:46"/><i><font color="Green">E99</font></i>: 
( <font color="Maroon">y3</font> <a href="hidden.html#R2">in</a>  <a href="fin_topo.html#K1">U_FT</a> <font color="Maroon">z2</font> &amp; <font color="Maroon">y3</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font> )
 
<b>by </b><i><a class="ref" href="fintopo6.html#T6" target="_self">Th6</a>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<b>reconsider </b><font color="Maroon">y4</font> = <font color="Maroon">y3</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">FT</font> <b>by </b><i><a class="txt" href="fintopo6.html#E4:46"><i><font color="Green">E41</font></i></a></i>;<br/>
<a NAME="E36:46"/>
<font color="Maroon">z2</font> <a href="hidden.html#R2">in</a>  <a href="fin_topo.html#K1">U_FT</a> <font color="Maroon">y4</font>
 
<b>by </b><i>, <a class="ref" href="fin_topo.html#D15">FIN_TOPO:def 15</a>, </i>;<br/>
<a NAME="E37:46"/><b>then </b>
<font color="Maroon">z2</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="fin_topo.html#K1">U_FT</a> <font color="Maroon">y4</font></span>)</span> <a href="subset_1.html#K9">/\</a> <font color="Maroon">Q2</font>
 
<b>by </b><i>, <a class="ref" href="fintopo6.html#T5" target="_self">Th5</a>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<a NAME="E38:46"/><b>then </b><i><font color="Green">E100</font></i>: 
 <a href="fin_topo.html#K1">U_FT</a> <font color="Maroon">y4</font> <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Maroon">Q2</font>
 
<b>by </b><i><a class="ref" href="xboole_0.html#D7">XBOOLE_0:def 7</a></i>;<br/>
<a NAME="E39:46"/><i><font color="Green">E101</font></i>: 
<font color="Maroon">y4</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font>
 
<b>by </b><i><a class="ref" href="fintopo6.html#T6" target="_self">Th6</a>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<b>set </b><font color="Maroon">P3</font> = <font color="Maroon">P2</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">C</font>;<br/>
<b>set </b><font color="Maroon">Q3</font> = <font color="Maroon">Q2</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">C</font>;<br/>
<i><font color="Green">E102</font></i>: <font color="Maroon">C</font> = 
<font color="Maroon">A</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">C</font>
<b>by </b><i><a class="txt" href="fintopo6.html#E1:46"><i><font color="Green">E27</font></i></a>, <a class="ref" href="xboole_1.html#T28">XBOOLE_1:28</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">P2</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">C</font></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><font color="Maroon">Q2</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">C</font></span>)</span>
<b>by </b><i>, <a class="ref" href="xboole_1.html#T23">XBOOLE_1:23</a></i>
;<br/>
<a NAME="E41:46"/>
<font color="Maroon">P2</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">C</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">P2</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T17">XBOOLE_1:17</a></i>;<br/>
<a NAME="E42:46"/><b>then </b><i><font color="Green">E105</font></i>: 
<font color="Maroon">P2</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">C</font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">Q2</font>
 
<b>by </b><i>, <a class="ref" href="xboole_1.html#T63">XBOOLE_1:63</a></i>;<br/>
<a NAME="E43:46"/>
<font color="Maroon">Q2</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">C</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">Q2</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T17">XBOOLE_1:17</a></i>;<br/>
<a NAME="E44:46"/><b>then </b><i><font color="Green">E106</font></i>: 
<font color="Maroon">P2</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">C</font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">Q2</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">C</font>
 
<b>by </b><i>, <a class="ref" href="xboole_1.html#T63">XBOOLE_1:63</a></i>;<br/>
<div><i><font color="Green">E107</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="46_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:46_2"/>
<font color="Maroon">P2</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">C</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/><a NAME="E2:46_2"/><b>then </b>
<font color="Maroon">y2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Q2</font>
 <b>by </b><i><a class="ref" href="fintopo6.html#T7" target="_self">Th7</a>, <a class="ref" href="fintopo6.html#T4" target="_self">Th4</a>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/><a NAME="E3:46_2"/><b>then </b>
<font color="Maroon">y2</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">P2</font> <a href="fin_topo.html#K9">^b</a> </span>)</span> <a href="subset_1.html#K9">/\</a> <font color="Maroon">Q2</font>
 <b>by </b><i><a class="ref" href="fintopo6.html#D1" target="_self">Def1</a>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/><b>hence </b><a NAME="E4:46_2"/>
contradiction
 <b>by </b><i>, <a class="ref" href="xboole_0.html#D7">XBOOLE_0:def 7</a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="46_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:46_3"/>
<font color="Maroon">Q2</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">C</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/><a NAME="E2:46_3"/><b>then </b><i><font color="Green">E108</font></i>: 
<font color="Maroon">y4</font> <a href="hidden.html#R2">in</a> <font color="Maroon">P2</font>
 <b>by </b><i><a class="ref" href="fintopo6.html#T7" target="_self">Th7</a>, , <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/><b>consider </b><font color="Maroon">w</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">FT</font><b> such that </b><br/><a NAME="E4:46_3"/><i><font color="Green">E109</font></i>: 
( <font color="Maroon">w</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y4</font> &amp;  <a href="fin_topo.html#K1">U_FT</a> <font color="Maroon">w</font> <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Maroon">Q2</font> )
 <b>by </b><i><a class="txt" href="fintopo6.html#E5:46"><i><font color="Green">E43</font></i></a></i>;<br/><b>consider </b><font color="Maroon">s</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E6:46_3"/><i><font color="Green">E110</font></i>: 
( <font color="Maroon">s</font> <a href="hidden.html#R2">in</a>  <a href="fin_topo.html#K1">U_FT</a> <font color="Maroon">w</font> &amp; <font color="Maroon">s</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Q2</font> )
 <b>by </b><i>, <a class="ref" href="xboole_0.html#T3">XBOOLE_0:3</a></i>;<br/><b>reconsider </b><font color="Maroon">s2</font> = <font color="Maroon">s</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">FT</font> <b>by </b><i><a class="ref" href="fintopo6.html#D3" target="_self">Def3</a></i>;<br/><a NAME="E8:46_3"/>
<font color="Maroon">w</font> <a href="hidden.html#R2">in</a>  <a href="fin_topo.html#K1">U_FT</a> <font color="Maroon">s2</font>
 <b>by </b><i><a class="ref" href="fintopo6.html#D3" target="_self">Def3</a>, <a class="ref" href="fin_topo.html#D15">FIN_TOPO:def 15</a>, </i>;<br/><a NAME="E9:46_3"/><b>then </b>
 <a href="fin_topo.html#K1">U_FT</a> <font color="Maroon">s2</font> <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Maroon">P2</font>
 <b>by </b><i><a class="ref" href="xboole_0.html#T3">XBOOLE_0:3</a>, , </i>;<br/><a NAME="E10:46_3"/><b>then </b>
<font color="Maroon">s2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">P2</font> <a href="fin_topo.html#K9">^b</a> 
 ;<br/><b>hence </b><a NAME="E11:46_3"/>
contradiction
 <b>by </b><i><a class="ref" href="fintopo6.html#D3" target="_self">Def3</a>, <a class="ref" href="xboole_0.html#T3">XBOOLE_0:3</a>, </i>;<br/></div><b>end;</b></div>
<a NAME="E47:46"/><b>then </b><i><font color="Green">E111</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">P2</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">C</font></span>)</span> <a href="fin_topo.html#K9">^b</a>  <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Maroon">Q2</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">C</font>
 
<b>by </b><i><a class="txt" href="fintopo6.html#E10"><i><font color="Green">Lemma48</font></i></a>, <a class="ref" href="fintopo6.html#T7" target="_self">Th7</a>, <a class="ref" href="fintopo6.html#D2" target="_self">Def2</a>, <a class="ref" href="fin_topo.html#D18">FIN_TOPO:def 18</a>, </i>;<br/>
<a NAME="E48:46"/>
<font color="Maroon">P2</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">C</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">P2</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T17">XBOOLE_1:17</a></i>;<br/>
<a NAME="E49:46"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">P2</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">C</font></span>)</span> <a href="fin_topo.html#K9">^b</a>  <a href="tarski.html#R1">c=</a> <font color="Maroon">P2</font> <a href="fin_topo.html#K9">^b</a> 
 
<b>by </b><i><a class="ref" href="fin_topo.html#T19">FIN_TOPO:19</a></i>;<br/>
<a NAME="E50:46"/><b>then </b><i><font color="Green">E112</font></i>: 
<font color="Maroon">P2</font> <a href="fin_topo.html#K9">^b</a>  <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Maroon">Q2</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">C</font>
 
<b>by </b><i>, <a class="ref" href="xboole_1.html#T63">XBOOLE_1:63</a></i>;<br/>
<a NAME="E51:46"/>
<font color="Maroon">Q2</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">C</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">Q2</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T17">XBOOLE_1:17</a></i>;<br/>
<b>hence </b><a NAME="E52:46"/>
contradiction
 <b>by </b><i>, , <a class="ref" href="xboole_1.html#T63">XBOOLE_1:63</a></i>;<br/>


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