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

<b>let </b><font color="Maroon">X</font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">Y</font> be   <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">X</font>;<br/><b>let </b><font color="Maroon">F</font> be    <a href="card_fil.html#M1" target="_self">Filter</a> of <font color="Maroon">X</font>;<br/>





<b>assume </b><a NAME="E1:8"/><i><font color="Green">E22</font></i>: 
<font color="Maroon">Y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F</font>
 ;<br/>

<b>assume </b><a NAME="E2:8"/>
<font color="Maroon">X</font> <a href="subset_1.html#K6">\</a> <font color="Maroon">Y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F</font>
 ;<br/>

<a NAME="E3:8"/><b>then </b><i><font color="Green">E24</font></i>: 
<font color="Maroon">Y</font> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="subset_1.html#K6">\</a> <font color="Maroon">Y</font></span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">F</font>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E4:8"/>
<font color="Maroon">Y</font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">X</font> <a href="subset_1.html#K6">\</a> <font color="Maroon">Y</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T79">XBOOLE_1:79</a></i>;<br/>
<a NAME="E5:8"/><b>then </b>
 <a href="xboole_0.html#K1">{}</a>  <a href="hidden.html#R2">in</a> <font color="Maroon">F</font>
 
<b>by </b><i>, <a class="ref" href="xboole_0.html#D7">XBOOLE_0:def 7</a></i>;<br/>
<b>hence </b><a NAME="E6:8"/>
contradiction
 <b>by </b><i/>;<br/>


</div>
