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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>assume </b><a NAME="E1:3"/>
not <span class="p1">(<span class="default"><a href="pre_topc.html#K1">{}</a> <font color="Maroon">FT</font></span>)</span> <a href="fin_topo.html#K9">^b</a>  <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/>

<b>then consider </b><font color="Maroon">x</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:3"/><i><font color="Green">E27</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K1">{}</a> <font color="Maroon">FT</font></span>)</span> <a href="fin_topo.html#K9">^b</a> 
 <b>by </b><i><a class="ref" href="xboole_0.html#D1">XBOOLE_0:def 1</a></i>;<br/>
<b>consider </b><font color="Maroon">y</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">FT</font><b> such that </b><br/><a NAME="E5:3"/><i><font color="Green">E31</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font> &amp;  <a href="fin_topo.html#K1">U_FT</a> <font color="Maroon">y</font> <a href="xboole_0.html#NR5" target="_self">meets</a>  <a href="pre_topc.html#K1">{}</a> <font color="Maroon">FT</font> )
 <b>by </b><i/>;<br/>
<b>thus </b><a NAME="E6:3"/>
contradiction
 <b>by </b><i><a class="ref" href="xboole_1.html#T65">XBOOLE_1:65</a>, </i>;<br/>


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