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

<b>let </b><font color="Maroon">X</font> be  <a href="finset_1.html#V1">infinite</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">F</font> be  <a href="card_fil.html#V3" target="_self">being_ultrafilter</a>  <a href="card_fil.html#M1" target="_self">Filter</a> of <font color="Maroon">X</font>;<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>thus </b><a NAME="E1:39"/>
( <font color="Maroon">Y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F</font> implies  not <font color="Maroon">Y</font> <a href="hidden.html#R2">in</a>  <a href="card_fil.html#K1" target="_self">dual</a> <font color="Maroon">F</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="39_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:39_1"/>
<font color="Maroon">Y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F</font>
 ;<br/>

<a NAME="E2:39_1"/><b>then </b>
not <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>
 
<b>by </b><i/>;<br/>
<a NAME="E3:39_1"/><b>then </b>
not <font color="Maroon">Y</font> <a href="subset_1.html#K3">`</a>  <a href="hidden.html#R2">in</a> <font color="Maroon">F</font>
 
;<br/>
<b>hence </b><a NAME="E4:39_1"/>
not <font color="Maroon">Y</font> <a href="hidden.html#R2">in</a>  <a href="card_fil.html#K1" target="_self">dual</a> <font color="Maroon">F</font>
 <b>by </b><i><a class="ref" href="setfam_1.html#D8">SETFAM_1:def 8</a></i>;<br/>


</div><b>end;</b></div>

<b>assume </b><a NAME="E2:39"/>
not <font color="Maroon">Y</font> <a href="hidden.html#R2">in</a>  <a href="card_fil.html#K1" target="_self">dual</a> <font color="Maroon">F</font>
 ;<br/>

<a NAME="E3:39"/><b>then </b>
not <font color="Maroon">Y</font> <a href="subset_1.html#K3">`</a>  <a href="hidden.html#R2">in</a> <font color="Maroon">F</font>
 
<b>by </b><i><a class="ref" href="setfam_1.html#D8">SETFAM_1:def 8</a></i>;<br/>
<a NAME="E4:39"/><b>then </b>
not <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/>
<b>hence </b><a NAME="E5:39"/>
<font color="Maroon">Y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F</font>
 <b>by </b><i/>;<br/>


</div>
