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<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">B</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">FT</font>;<br/>



<b>assume </b><a NAME="E1:51"/><i><font color="Green">E27</font></i>: 
( <font color="Maroon">FT</font> is <a href="fin_topo.html#V2">symmetric</a> &amp; <font color="Maroon">A</font> <a href="fintopo6.html#R1" target="_self">is_a_component_of</a> <font color="Maroon">FT</font> &amp; <font color="Maroon">B</font> <a href="fintopo6.html#R1" target="_self">is_a_component_of</a> <font color="Maroon">FT</font> )
 ;<br/>

<b>assume </b><b>that </b><br/><a NAME="E2:51"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">A</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">B</font>
 <b>and </b><br/><a NAME="E3:51"/><i><font color="Green">E33</font></i>: 
not <font color="Maroon">A</font>,<font color="Maroon">B</font> <a href="fintopo4.html#R1">are_separated</a> 
 ;<br/>

<a NAME="E4:51"/>
( <font color="Maroon">A</font> is <a href="fin_topo.html#V5">connected</a> &amp; <font color="Maroon">B</font> is <a href="fin_topo.html#V5">connected</a> )
 
<b>by </b><i>, </i>;<br/>
<a NAME="E5:51"/><b>then </b><i><font color="Green">E41</font></i>: 
<font color="Maroon">A</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">B</font> is <a href="fin_topo.html#V5">connected</a>
 
<b>by </b><i>, <a class="txt" href="fintopo6.html#E2:51"><i><font color="Green">E31</font></i></a>, </i>;<br/>
<a NAME="E6:51"/>
( <font color="Maroon">A</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">A</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">B</font> &amp; <font color="Maroon">B</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">A</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">B</font> )
 
<b>by </b><i><a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a></i>;<br/>
<a NAME="E7:51"/><b>then </b>
( <font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <font color="Maroon">A</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">B</font> &amp; <font color="Maroon">B</font> <a href="hidden.html#R1">=</a> <font color="Maroon">A</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">B</font> )
 
<b>by </b><i>, , </i>;<br/>
<b>hence </b><a NAME="E8:51"/>
contradiction
 <b>by </b><i/>;<br/>


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