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

<span class="kw">let </span><font color="Maroon" title="c1">FT</font> be   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">A</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">FT</font> holds <br/> ( <font color="Olive" title="b1">A</font> is  <a href="fin_topo.html#V4" title="FIN_TOPO:attr.4">connected</a>  iff <font color="Maroon" title="c1">FT</font> <a href="fintopo6.html#K1" title="FINTOPO6:func.1">|</a> <font color="Olive" title="b1">A</font> is  <a href="fintopo6.html#V1" title="FINTOPO6:attr.1">connected</a>  )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">A</font> be   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">FT</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">A</font> is  <a href="fin_topo.html#V4" title="FIN_TOPO:attr.4">connected</a>  iff <font color="Maroon" title="c1">FT</font> <a href="fintopo6.html#K1" title="FINTOPO6:func.1">|</a> <font color="Maroon" title="c2">A</font> is  <a href="fintopo6.html#V1" title="FINTOPO6:attr.1">connected</a>  )</span><br/>



<a NAME="E1:24"/><span class="lab"><font color="Green" title="E13">A1</font></span>: 
 <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">FT</font> <a href="fintopo6.html#K1" title="FINTOPO6:func.1">|</a> <font color="Maroon" title="c2">A</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="fintopo6.html#D3" target="_self" onmouseover="rs('fintopo6/D3')" onmouseout="rh()">Def3</a></span>;<br/>
<span class="kw">thus </span><a NAME="E2:24"/>
( <font color="Maroon" title="c2">A</font> is  <a href="fin_topo.html#V4" title="FIN_TOPO:attr.4">connected</a>  implies <font color="Maroon" title="c1">FT</font> <a href="fintopo6.html#K1" title="FINTOPO6:func.1">|</a> <font color="Maroon" title="c2">A</font> is  <a href="fintopo6.html#V1" title="FINTOPO6:attr.1">connected</a>  )
  <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">FT</font> <a href="fintopo6.html#K1" title="FINTOPO6:func.1">|</a> <font color="Maroon" title="c2">A</font> is  <a href="fintopo6.html#V1" title="FINTOPO6:attr.1">connected</a>  implies <font color="Maroon" title="c2">A</font> is  <a href="fin_topo.html#V4" title="FIN_TOPO:attr.4">connected</a>  )</span><div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="24_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:24_1"/><span class="lab"><font color="Green" title="E14">A2</font></span>: 
<font color="Maroon" title="c2">A</font> is  <a href="fin_topo.html#V4" title="FIN_TOPO:attr.4">connected</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">FT</font> <a href="fintopo6.html#K1" title="FINTOPO6:func.1">|</a> <font color="Maroon" title="c2">A</font> is  <a href="fintopo6.html#V1" title="FINTOPO6:attr.1">connected</a> </span><br/>

<a NAME="E2:24_1"/>
 for <font color="Olive" title="b1">B2</font>, <font color="Olive" title="b2">C2</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">FT</font> <a href="fintopo6.html#K1" title="FINTOPO6:func.1">|</a> <font color="Maroon" title="c2">A</font></span>)</span>  st  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">FT</font> <a href="fintopo6.html#K1" title="FINTOPO6:func.1">|</a> <font color="Maroon" title="c2">A</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">B2</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Olive" title="b2">C2</font> &amp; <font color="Olive" title="b1">B2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Olive" title="b2">C2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Olive" title="b1">B2</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Olive" title="b2">C2</font> holds <br/><font color="Olive" title="b1">B2</font> <a href="fin_topo.html#K9" title="FIN_TOPO:func.9">^b</a>  <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a> <font color="Olive" title="b2">C2</font>
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="24_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c3">B2</font>, <font color="Maroon" title="c4">C2</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">FT</font> <a href="fintopo6.html#K1" title="FINTOPO6:func.1">|</a> <font color="Maroon" title="c2">A</font></span>)</span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">FT</font> <a href="fintopo6.html#K1" title="FINTOPO6:func.1">|</a> <font color="Maroon" title="c2">A</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">B2</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c4">C2</font> &amp; <font color="Maroon" title="c3">B2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c4">C2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c3">B2</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Maroon" title="c4">C2</font> implies <font color="Maroon" title="c3">B2</font> <a href="fin_topo.html#K9" title="FIN_TOPO:func.9">^b</a>  <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a> <font color="Maroon" title="c4">C2</font> )</span><br/>

<a NAME="E1:24_1_1"/><span class="lab"><font color="Green" title="E15">A3</font></span>: 
<span class="p1">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">FT</font> <a href="fintopo6.html#K1" title="FINTOPO6:func.1">|</a> <font color="Maroon" title="c2">A</font></span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c4">C2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">C2</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T28" onmouseover="rs('xboole_1/T28')" onmouseout="rh()">XBOOLE_1:28</a></span>;<br/>
 the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">FT</font> <a href="fintopo6.html#K1" title="FINTOPO6:func.1">|</a> <font color="Maroon" title="c2">A</font></span>)</span> = 
 <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">FT</font> <a href="fintopo6.html#K1" title="FINTOPO6:func.1">|</a> <font color="Maroon" title="c2">A</font></span>)</span>

<br/>.= 
<font color="Maroon" title="c2">A</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="fintopo6.html#D3" target="_self" onmouseover="rs('fintopo6/D3')" onmouseout="rh()">Def3</a></span>
;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c5">B3</font> = <font color="Maroon" title="c3">B2</font>, <font color="Maroon" title="c6">C3</font> = <font color="Maroon" title="c4">C2</font> as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">FT</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T1" onmouseover="rs('xboole_1/T1')" onmouseout="rh()">XBOOLE_1:1</a></span>;<br/>
<span class="kw">assume </span><a NAME="E4:24_1_1"/>
(  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">FT</font> <a href="fintopo6.html#K1" title="FINTOPO6:func.1">|</a> <font color="Maroon" title="c2">A</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">B2</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c4">C2</font> &amp; <font color="Maroon" title="c3">B2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c4">C2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c3">B2</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Maroon" title="c4">C2</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">B2</font> <a href="fin_topo.html#K9" title="FIN_TOPO:func.9">^b</a>  <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a> <font color="Maroon" title="c4">C2</font></span><br/>

<a NAME="E5:24_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E16">A4</font></span>: 
<font color="Maroon" title="c5">B3</font> <a href="fin_topo.html#K9" title="FIN_TOPO:func.9">^b</a>  <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a> <font color="Maroon" title="c6">C3</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:24"><span class="lab"><font color="Green" title="E13">A1</font></span></a>, <a class="txt" href="#E1:24_1"><span class="lab"><font color="Green" title="E14">A2</font></span></a></span>;<br/>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">B2</font> <a href="fin_topo.html#K9" title="FIN_TOPO:func.9">^b</a></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c4">C2</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">B3</font> <a href="fin_topo.html#K9" title="FIN_TOPO:func.9">^b</a></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p2">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">FT</font> <a href="fintopo6.html#K1" title="FINTOPO6:func.1">|</a> <font color="Maroon" title="c2">A</font></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c4">C2</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="fintopo6.html#T13" target="_self" onmouseover="rs('fintopo6/T13')" onmouseout="rh()">Th12</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">B3</font> <a href="fin_topo.html#K9" title="FIN_TOPO:func.9">^b</a></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c6">C3</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:24_1_1"><span class="lab"><font color="Green" title="E15">A3</font></span></a>, <a class="ref" href="xboole_1.html#T16" onmouseover="rs('xboole_1/T16')" onmouseout="rh()">XBOOLE_1:16</a></span>
;<br/>
<a NAME="E7:24_1_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">B2</font> <a href="fin_topo.html#K9" title="FIN_TOPO:func.9">^b</a></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c4">C2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:24_1_1"><span class="lab"><font color="Green" title="E16">A4</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E8:24_1_1"/>
<font color="Maroon" title="c3">B2</font> <a href="fin_topo.html#K9" title="FIN_TOPO:func.9">^b</a>  <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a> <font color="Maroon" title="c4">C2</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E3:24_1"/><span class="kw">then </span>
 <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">FT</font> <a href="fintopo6.html#K1" title="FINTOPO6:func.1">|</a> <font color="Maroon" title="c2">A</font></span>)</span> is  <a href="fin_topo.html#V4" title="FIN_TOPO:attr.4">connected</a> 
 
;<br/>
<span class="kw">hence </span><a NAME="E4:24_1"/>
<font color="Maroon" title="c1">FT</font> <a href="fintopo6.html#K1" title="FINTOPO6:func.1">|</a> <font color="Maroon" title="c2">A</font> is  <a href="fintopo6.html#V1" title="FINTOPO6:attr.1">connected</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>

<span class="kw">assume </span><a NAME="E3:24"/>
<font color="Maroon" title="c1">FT</font> <a href="fintopo6.html#K1" title="FINTOPO6:func.1">|</a> <font color="Maroon" title="c2">A</font> is  <a href="fintopo6.html#V1" title="FINTOPO6:attr.1">connected</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">A</font> is  <a href="fin_topo.html#V4" title="FIN_TOPO:attr.4">connected</a> </span><br/>

<a NAME="E4:24"/><span class="kw">then </span><span class="lab"><font color="Green" title="E14">A5</font></span>: 
 <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">FT</font> <a href="fintopo6.html#K1" title="FINTOPO6:func.1">|</a> <font color="Maroon" title="c2">A</font></span>)</span> is  <a href="fin_topo.html#V4" title="FIN_TOPO:attr.4">connected</a> 
 
;<br/>
<span class="kw">let </span><font color="Maroon" title="c3">B</font>, <font color="Maroon" title="c4">C</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">FT</font>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="fin_topo.html#D16" onmouseover="rs('fin_topo/D16')" onmouseout="rh()">FIN_TOPO:def 16</a> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c2">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">B</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c4">C</font> or <font color="Maroon" title="c3">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  or <font color="Maroon" title="c4">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  or  not <font color="Maroon" title="c3">B</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Maroon" title="c4">C</font> or  not <font color="Maroon" title="c3">B</font> <a href="fin_topo.html#K9" title="FIN_TOPO:func.9">^b</a>  <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Maroon" title="c4">C</font> )</span><br/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E5:24"/><span class="lab"><font color="Green" title="E15">A6</font></span>: 
<font color="Maroon" title="c2">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">B</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c4">C</font>
 <span class="kw">and </span><br/><a NAME="E6:24"/><span class="lab"><font color="Green" title="E16">A7</font></span>: 
( <font color="Maroon" title="c3">B</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c4">C</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c3">B</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Maroon" title="c4">C</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  not <font color="Maroon" title="c3">B</font> <a href="fin_topo.html#K9" title="FIN_TOPO:func.9">^b</a>  <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Maroon" title="c4">C</font></span><br/>

<a NAME="E7:24"/><span class="lab"><font color="Green" title="E17">A8</font></span>: 
 <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">FT</font> <a href="fintopo6.html#K1" title="FINTOPO6:func.1">|</a> <font color="Maroon" title="c2">A</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="fintopo6.html#D3" target="_self" onmouseover="rs('fintopo6/D3')" onmouseout="rh()">Def3</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c5">B2</font> = <font color="Maroon" title="c3">B</font> as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">FT</font> <a href="fintopo6.html#K1" title="FINTOPO6:func.1">|</a> <font color="Maroon" title="c2">A</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:24"><span class="lab"><font color="Green" title="E15">A6</font></span></a>, <a class="ref" href="xboole_1.html#T7" onmouseover="rs('xboole_1/T7')" onmouseout="rh()">XBOOLE_1:7</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c6">C2</font> = <font color="Maroon" title="c4">C</font> as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">FT</font> <a href="fintopo6.html#K1" title="FINTOPO6:func.1">|</a> <font color="Maroon" title="c2">A</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:24"><span class="lab"><font color="Green" title="E15">A6</font></span></a>, <a class="txt" href="#E7:24"><span class="lab"><font color="Green" title="E17">A8</font></span></a>, <a class="ref" href="xboole_1.html#T7" onmouseover="rs('xboole_1/T7')" onmouseout="rh()">XBOOLE_1:7</a></span>;<br/>
<a NAME="E10:24"/>
( <span class="p1">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">FT</font> <a href="fintopo6.html#K1" title="FINTOPO6:func.1">|</a> <font color="Maroon" title="c2">A</font></span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c6">C2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">C2</font> &amp; <font color="Maroon" title="c5">B2</font> <a href="fin_topo.html#K9" title="FIN_TOPO:func.9">^b</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">B</font> <a href="fin_topo.html#K9" title="FIN_TOPO:func.9">^b</a></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">FT</font> <a href="fintopo6.html#K1" title="FINTOPO6:func.1">|</a> <font color="Maroon" title="c2">A</font></span>)</span></span>)</span> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="fintopo6.html#T13" target="_self" onmouseover="rs('fintopo6/T13')" onmouseout="rh()">Th12</a>, <a class="ref" href="xboole_1.html#T28" onmouseover="rs('xboole_1/T28')" onmouseout="rh()">XBOOLE_1:28</a></span>;<br/>
<a NAME="E11:24"/><span class="kw">then </span><span class="lab"><font color="Green" title="E18">A9</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">B</font> <a href="fin_topo.html#K9" title="FIN_TOPO:func.9">^b</a></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c4">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">B2</font> <a href="fin_topo.html#K9" title="FIN_TOPO:func.9">^b</a></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c6">C2</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T16" onmouseover="rs('xboole_1/T16')" onmouseout="rh()">XBOOLE_1:16</a></span>;<br/>
<a NAME="E12:24"/>
<font color="Maroon" title="c5">B2</font> <a href="fin_topo.html#K9" title="FIN_TOPO:func.9">^b</a>  <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a> <font color="Maroon" title="c6">C2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:24"><span class="lab"><font color="Green" title="E14">A5</font></span></a>, <a class="txt" href="#E5:24"><span class="lab"><font color="Green" title="E15">A6</font></span></a>, <a class="txt" href="#E6:24"><span class="lab"><font color="Green" title="E16">A7</font></span></a>, <a class="txt" href="#E7:24"><span class="lab"><font color="Green" title="E17">A8</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E13:24"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">B</font> <a href="fin_topo.html#K9" title="FIN_TOPO:func.9">^b</a></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c4">C</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:24"><span class="lab"><font color="Green" title="E18">A9</font></span></a></span>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="xboole_0.html#D7" onmouseover="rs('xboole_0/D7')" onmouseout="rh()">XBOOLE_0:def 7</a> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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