<?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>;<br/><b>let </b><font color="Maroon">C</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">FT</font>;<br/><b>let </b><font color="Maroon">D</font> be  non <a href="xboole_0.html#V1">empty</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">FT</font>;<br/>







<b>assume </b><b>that </b><br/><a NAME="E1:55"/><i><font color="Green">E27</font></i>: 
( <font color="Maroon">FT</font> is <a href="fin_topo.html#V1">filled</a> &amp; <font color="Maroon">FT</font> is <a href="fin_topo.html#V2">symmetric</a> &amp; <font color="Maroon">D</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K2">[#]</a> <font color="Maroon">FT</font></span>)</span> <a href="subset_1.html#K7">\</a> <font color="Maroon">A</font> &amp; <font color="Maroon">FT</font> is <a href="fintopo6.html#V1" target="_self">connected</a> )
 <b>and </b><br/><a NAME="E2:55"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">A</font> is <a href="fin_topo.html#V5">connected</a>
 <b>and </b><br/><a NAME="E3:55"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">C</font> <a href="fintopo6.html#R2" target="_self">is_a_component_of</a> <font color="Maroon">D</font>
 ;<br/>

<b>consider </b><font color="Maroon">C1</font> being   <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><font color="Maroon">FT</font> <a href="fintopo6.html#K1" target="_self">|</a> <font color="Maroon">D</font></span>)</span><b> such that </b><br/><a NAME="E5:55"/><i><font color="Green">E41</font></i>: 
<font color="Maroon">C1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">C</font>
 <b>and </b><br/><a NAME="E6:55"/><i><font color="Green">E43</font></i>: 
<font color="Maroon">C1</font> <a href="fintopo6.html#R1" target="_self">is_a_component_of</a> <font color="Maroon">FT</font> <a href="fintopo6.html#K1" target="_self">|</a> <font color="Maroon">D</font>
 <b>by </b><i>, </i>;<br/>
<a NAME="E7:55"/><i><font color="Green">E57</font></i>: 
<font color="Maroon">C1</font> is <a href="fin_topo.html#V5">connected</a>
 
<b>by </b><i><a class="ref" href="fintopo6.html#T2" target="_self">Th2</a>, </i>;<br/>
<b>reconsider </b><font color="Maroon">C2</font> = <font color="Maroon">C1</font> as   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">FT</font> <b>by </b><i><a class="txt" href="fintopo6.html#E3:55"><i><font color="Green">E33</font></i></a></i>;<br/>
<a NAME="E9:55"/>
<font color="Maroon">C1</font> <a href="tarski.html#R1">c=</a>  <a href="pre_topc.html#K2">[#]</a> <span class="p1">(<span class="default"><font color="Maroon">FT</font> <a href="fintopo6.html#K1" target="_self">|</a> <font color="Maroon">D</font></span>)</span>
 
;<br/>
<a NAME="E10:55"/><b>then </b>
<font color="Maroon">C1</font> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K2">[#]</a> <font color="Maroon">FT</font></span>)</span> <a href="subset_1.html#K7">\</a> <font color="Maroon">A</font>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E11:55"/><b>then </b><i><font color="Green">E60</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pre_topc.html#K2">[#]</a> <font color="Maroon">FT</font></span>)</span> <a href="subset_1.html#K7">\</a> <font color="Maroon">A</font></span>)</span> <a href="subset_1.html#K3">`</a>  <a href="tarski.html#R1">c=</a> <font color="Maroon">C2</font> <a href="subset_1.html#K3">`</a> 
 
<b>by </b><i><a class="ref" href="subset_1.html#T31">SUBSET_1:31</a></i>;<br/>
<a NAME="E12:55"/><b>then </b><i><font color="Green">E71</font></i>: 
<font color="Maroon">A</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">C2</font> <a href="subset_1.html#K3">`</a> 
 
<b>by </b><i><a class="ref" href="pre_topc.html#T22">PRE_TOPC:22</a></i>;<br/>
<a NAME="E13:55"/><i><font color="Green">E81</font></i>: 
<font color="Maroon">A</font> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K2">[#]</a> <font color="Maroon">FT</font></span>)</span> <a href="subset_1.html#K7">\</a> <font color="Maroon">C2</font>
 
<b>by </b><i><a class="ref" href="fintopo6.html#D1" target="_self">Def1</a>, <a class="ref" href="pre_topc.html#T22">PRE_TOPC:22</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="55_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">P</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">FT</font>, <font color="Maroon">Q</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="E1:55_1"/><i><font color="Green">E82</font></i>: 
<span class="p1">(<span class="default"><a href="pre_topc.html#K2">[#]</a> <font color="Maroon">FT</font></span>)</span> <a href="subset_1.html#K7">\</a> <font color="Maroon">C</font> <a href="hidden.html#R1">=</a> <font color="Maroon">P</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">Q</font>
 <b>and </b><br/><a NAME="E2:55_1"/><i><font color="Green">E83</font></i>: 
<font color="Maroon">P</font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">Q</font>
 <b>and </b><br/><a NAME="E3:55_1"/><i><font color="Green">E84</font></i>: 
<font color="Maroon">P</font>,<font color="Maroon">Q</font> <a href="fintopo4.html#R1">are_separated</a> 
 ;<br/><a NAME="E4:55_1"/><i><font color="Green">E85</font></i>: 
<font color="Maroon">Q</font> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K2">[#]</a> <font color="Maroon">FT</font></span>)</span> <a href="subset_1.html#K7">\</a> <font color="Maroon">C</font>
 <b>by </b><i><a class="ref" href="fintopo6.html#T5" target="_self">Th5</a>, <a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a></i>;<br/><a NAME="E5:55_1"/>
<font color="Maroon">A</font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">C1</font>
 <b>by </b><i><a class="ref" href="fintopo6.html#T4" target="_self">Th4</a>, <a class="ref" href="subset_1.html#T43">SUBSET_1:43</a></i>;<br/><a NAME="E6:55_1"/><b>then </b><i><font color="Green">E86</font></i>: 
<font color="Maroon">A</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">C1</font> <a href="hidden.html#R1">=</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/><a NAME="E7:55_1"/><i><font color="Green">E87</font></i>: 
<font color="Maroon">C</font> is <a href="fin_topo.html#V5">connected</a>
 <b>by </b><i>, <a class="txt" href="fintopo6.html#E3:55"><i><font color="Green">E33</font></i></a>, <a class="ref" href="fintopo6.html#T3" target="_self">Th3</a>, <a class="txt" href="fintopo6.html#E1:55"><i><font color="Green">E27</font></i></a></i>;<br/><a NAME="E8:55_1"/><i><font color="Green">E97</font></i>: 
<font color="Maroon">P</font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">P</font> <a href="subset_1.html#K3">`</a> 
 <b>by </b><i><a class="ref" href="xboole_1.html#T79">XBOOLE_1:79</a></i>;<br/><div><i><font color="Green">E98</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="55_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:55_1_1"/><i><font color="Green">E99</font></i>: 
<font color="Maroon">A</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">P</font>
 ;<br/><a NAME="E2:55_1_1"/>
<font color="Maroon">Q</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">P</font> <a href="subset_1.html#K3">`</a> 
 <b>by </b><i><a class="ref" href="fintopo6.html#T6" target="_self">Th6</a>, <a class="ref" href="subset_1.html#T43">SUBSET_1:43</a></i>;<br/><a NAME="E3:55_1_1"/><b>then </b>
<font color="Maroon">A</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">Q</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">P</font> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><font color="Maroon">P</font> <a href="subset_1.html#K3">`</a> </span>)</span>
 <b>by </b><i><a class="ref" href="fintopo6.html#D2" target="_self">Def2</a>, <a class="ref" href="xboole_1.html#T27">XBOOLE_1:27</a></i>;<br/><a NAME="E4:55_1_1"/><b>then </b><i><font color="Green">E100</font></i>: 
<font color="Maroon">A</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">Q</font> <a href="tarski.html#R1">c=</a>  <a href="xboole_0.html#K1">{}</a> 
 <b>by </b><i><a class="ref" href="fintopo6.html#T7" target="_self">Th7</a>, <a class="ref" href="xboole_0.html#D7">XBOOLE_0:def 7</a></i>;<br/><span class="p1">(<span class="default"><font color="Maroon">C</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">Q</font></span>)</span> <a href="subset_1.html#K9">/\</a> <font color="Maroon">A</font> = 
<span class="p1">(<span class="default"><font color="Maroon">A</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">A</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">Q</font></span>)</span>
<b>by </b><i><a class="ref" href="xboole_1.html#T23">XBOOLE_1:23</a></i>
<br/>.= 
 <a href="xboole_0.html#K1">{}</a> 
<b>by </b><i><a class="txt" href="fintopo6.html#E3:55"><i><font color="Green">E33</font></i></a>, <a class="txt" href="fintopo6.html#E6:55"><i><font color="Green">E43</font></i></a>, <a class="txt" href="fintopo6.html#E10"><i><font color="Green">Lemma48</font></i></a>, <a class="ref" href="xboole_1.html#T3">XBOOLE_1:3</a></i>
;<br/><a NAME="E6:55_1_1"/><b>then </b>
<font color="Maroon">C</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">Q</font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">A</font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D7">XBOOLE_0:def 7</a></i>;<br/><a NAME="E7:55_1_1"/><b>then </b>
<font color="Maroon">C</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">Q</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">A</font> <a href="subset_1.html#K3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43">SUBSET_1:43</a></i>;<br/><a NAME="E8:55_1_1"/><b>then </b>
<font color="Maroon">C</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">Q</font> <a href="tarski.html#R1">c=</a>  <a href="pre_topc.html#K2">[#]</a> <span class="p1">(<span class="default"><font color="Maroon">FT</font> <a href="fintopo6.html#K1" target="_self">|</a> <font color="Maroon">D</font></span>)</span>
 <b>by </b><i>, </i>;<br/><b>then reconsider </b><font color="Maroon">C1Q1</font> = <font color="Maroon">C</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">Q</font> as   <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><font color="Maroon">FT</font> <a href="fintopo6.html#K1" target="_self">|</a> <font color="Maroon">D</font></span>)</span> ;<br/><a NAME="E10:55_1_1"/>
<font color="Maroon">C</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">Q</font> is <a href="fin_topo.html#V5">connected</a>
 <b>by </b><i>, <a class="ref" href="fintopo6.html#T5" target="_self">Th5</a>, <a class="txt" href="fintopo6.html#E5:55"><i><font color="Green">E41</font></i></a>, , </i>;<br/><a NAME="E11:55_1_1"/><b>then </b><i><font color="Green">E101</font></i>: 
<font color="Maroon">C1Q1</font> is <a href="fin_topo.html#V5">connected</a>
 <b>by </b><i><a class="txt" href="fintopo6.html#E1:55"><i><font color="Green">E27</font></i></a>, </i>;<br/><a NAME="E12:55_1_1"/><i><font color="Green">E102</font></i>: 
<font color="Maroon">C</font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">C</font> <a href="subset_1.html#K3">`</a> 
 <b>by </b><i><a class="ref" href="xboole_1.html#T79">XBOOLE_1:79</a></i>;<br/><a NAME="E13:55_1_1"/>
<font color="Maroon">C1</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">C1</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">Q</font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a></i>;<br/><a NAME="E14:55_1_1"/><b>then </b>
<font color="Maroon">C1Q1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">C1</font>
 <b>by </b><i><a class="txt" href="fintopo6.html#E3:55"><i><font color="Green">E33</font></i></a>, <a class="ref" href="fintopo6.html#T2" target="_self">Th2</a>, , </i>;<br/><a NAME="E15:55_1_1"/><b>then </b>
<font color="Maroon">Q</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">C</font>
 <b>by </b><i><a class="txt" href="fintopo6.html#E3:55"><i><font color="Green">E33</font></i></a>, <a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a></i>;<br/><a NAME="E16:55_1_1"/><b>then </b>
<font color="Maroon">Q</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">C</font> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pre_topc.html#K2">[#]</a> <font color="Maroon">FT</font></span>)</span> <a href="subset_1.html#K7">\</a> <font color="Maroon">C</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="xboole_1.html#T19">XBOOLE_1:19</a></i>;<br/><a NAME="E17:55_1_1"/><b>then </b>
<font color="Maroon">Q</font> <a href="tarski.html#R1">c=</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>hence </b><a NAME="E18:55_1_1"/>
<font color="Maroon">Q</font> <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#K1">{}</a> <font color="Maroon">FT</font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T3">XBOOLE_1:3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="55_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:55_1_2"/><i><font color="Green">E105</font></i>: 
<font color="Maroon">A</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">Q</font>
 ;<br/><a NAME="E2:55_1_2"/><i><font color="Green">E106</font></i>: 
<font color="Maroon">Q</font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">Q</font> <a href="subset_1.html#K3">`</a> 
 <b>by </b><i><a class="ref" href="xboole_1.html#T79">XBOOLE_1:79</a></i>;<br/><a NAME="E3:55_1_2"/>
<font color="Maroon">P</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">Q</font> <a href="subset_1.html#K3">`</a> 
 <b>by </b><i><a class="ref" href="fintopo6.html#T6" target="_self">Th6</a>, <a class="ref" href="subset_1.html#T43">SUBSET_1:43</a></i>;<br/><a NAME="E4:55_1_2"/><b>then </b>
<font color="Maroon">A</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">P</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">Q</font> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><font color="Maroon">Q</font> <a href="subset_1.html#K3">`</a> </span>)</span>
 <b>by </b><i><a class="ref" href="fintopo6.html#D2" target="_self">Def2</a>, <a class="ref" href="xboole_1.html#T27">XBOOLE_1:27</a></i>;<br/><a NAME="E5:55_1_2"/><b>then </b><i><font color="Green">E107</font></i>: 
<font color="Maroon">A</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">P</font> <a href="tarski.html#R1">c=</a>  <a href="xboole_0.html#K1">{}</a> 
 <b>by </b><i><a class="txt" href="fintopo6.html#E10"><i><font color="Green">Lemma48</font></i></a>, <a class="ref" href="xboole_0.html#D7">XBOOLE_0:def 7</a></i>;<br/><span class="p1">(<span class="default"><font color="Maroon">C</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">P</font></span>)</span> <a href="subset_1.html#K9">/\</a> <font color="Maroon">A</font> = 
<span class="p1">(<span class="default"><font color="Maroon">A</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">A</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">P</font></span>)</span>
<b>by </b><i><a class="ref" href="xboole_1.html#T23">XBOOLE_1:23</a></i>
<br/>.= 
 <a href="xboole_0.html#K1">{}</a> 
<b>by </b><i><a class="txt" href="fintopo6.html#E3:55"><i><font color="Green">E33</font></i></a>, <a class="txt" href="fintopo6.html#E6:55"><i><font color="Green">E43</font></i></a>, , <a class="ref" href="xboole_1.html#T3">XBOOLE_1:3</a></i>
;<br/><a NAME="E7:55_1_2"/><b>then </b>
<font color="Maroon">C</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">P</font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">A</font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D7">XBOOLE_0:def 7</a></i>;<br/><a NAME="E8:55_1_2"/><b>then </b>
<font color="Maroon">C</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">P</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">A</font> <a href="subset_1.html#K3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43">SUBSET_1:43</a></i>;<br/><a NAME="E9:55_1_2"/><b>then </b>
<font color="Maroon">C</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">P</font> <a href="tarski.html#R1">c=</a>  <a href="pre_topc.html#K2">[#]</a> <span class="p1">(<span class="default"><font color="Maroon">FT</font> <a href="fintopo6.html#K1" target="_self">|</a> <font color="Maroon">D</font></span>)</span>
 <b>by </b><i>, </i>;<br/><b>then reconsider </b><font color="Maroon">C1P1</font> = <font color="Maroon">C</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">P</font> as   <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><font color="Maroon">FT</font> <a href="fintopo6.html#K1" target="_self">|</a> <font color="Maroon">D</font></span>)</span> ;<br/><a NAME="E11:55_1_2"/>
<font color="Maroon">C</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">P</font> is <a href="fin_topo.html#V5">connected</a>
 <b>by </b><i>, <a class="ref" href="fintopo6.html#T5" target="_self">Th5</a>, <a class="txt" href="fintopo6.html#E5:55"><i><font color="Green">E41</font></i></a>, , </i>;<br/><a NAME="E12:55_1_2"/><b>then </b><i><font color="Green">E108</font></i>: 
<font color="Maroon">C1P1</font> is <a href="fin_topo.html#V5">connected</a>
 <b>by </b><i><a class="txt" href="fintopo6.html#E1:55"><i><font color="Green">E27</font></i></a>, </i>;<br/><a NAME="E13:55_1_2"/>
<font color="Maroon">C</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">C1</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">P</font>
 <b>by </b><i><a class="txt" href="fintopo6.html#E3:55"><i><font color="Green">E33</font></i></a>, <a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a></i>;<br/><a NAME="E14:55_1_2"/><b>then </b>
<font color="Maroon">C1P1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">C1</font>
 <b>by </b><i><a class="txt" href="fintopo6.html#E3:55"><i><font color="Green">E33</font></i></a>, <a class="ref" href="fintopo6.html#T2" target="_self">Th2</a>, , </i>;<br/><a NAME="E15:55_1_2"/><b>then </b><i><font color="Green">E109</font></i>: 
<font color="Maroon">P</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">C</font>
 <b>by </b><i><a class="txt" href="fintopo6.html#E3:55"><i><font color="Green">E33</font></i></a>, <a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a></i>;<br/><a NAME="E16:55_1_2"/><i><font color="Green">E110</font></i>: 
<font color="Maroon">C</font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">C</font> <a href="subset_1.html#K3">`</a> 
 <b>by </b><i><a class="ref" href="xboole_1.html#T79">XBOOLE_1:79</a></i>;<br/><a NAME="E17:55_1_2"/>
<font color="Maroon">P</font> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K2">[#]</a> <font color="Maroon">FT</font></span>)</span> <a href="subset_1.html#K7">\</a> <font color="Maroon">C</font>
 <b>by </b><i><a class="ref" href="fintopo6.html#T5" target="_self">Th5</a>, <a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a></i>;<br/><a NAME="E18:55_1_2"/><b>then </b>
<font color="Maroon">P</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">C</font> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pre_topc.html#K2">[#]</a> <font color="Maroon">FT</font></span>)</span> <a href="subset_1.html#K7">\</a> <font color="Maroon">C</font></span>)</span>
 <b>by </b><i><a class="ref" href="fintopo6.html#D3" target="_self">Def3</a>, <a class="ref" href="xboole_1.html#T19">XBOOLE_1:19</a></i>;<br/><a NAME="E19:55_1_2"/><b>then </b>
<font color="Maroon">P</font> <a href="tarski.html#R1">c=</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>hence </b><a NAME="E20:55_1_2"/>
<font color="Maroon">P</font> <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#K1">{}</a> <font color="Maroon">FT</font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T3">XBOOLE_1:3</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E11:55_1"/>
( <font color="Maroon">P</font> <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#K1">{}</a> <font color="Maroon">FT</font> or <font color="Maroon">Q</font> <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#K1">{}</a> <font color="Maroon">FT</font> )
 <b>by </b><i>, <a class="txt" href="fintopo6.html#E2:55"><i><font color="Green">E31</font></i></a>, <a class="txt" href="fintopo6.html#E3:55"><i><font color="Green">E33</font></i></a>, , <a class="ref" href="fintopo6.html#T5" target="_self">Th5</a>, <a class="txt" href="fintopo6.html#E5:55"><i><font color="Green">E41</font></i></a>, , </i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E15:55"/>
<span class="p1">(<span class="default"><a href="pre_topc.html#K2">[#]</a> <font color="Maroon">FT</font></span>)</span> <a href="subset_1.html#K7">\</a> <font color="Maroon">C</font> is <a href="fin_topo.html#V5">connected</a>
 <b>by </b><i>, </i>;<br/>


</div>
