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<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">Uf</font> be    <a href="card_fil.html#M1" target="_self">Filter</a> of <font color="Maroon">X</font>;<br/>



<b>assume </b><a NAME="E1:36"/><i><font color="Green">E22</font></i>: 
( <font color="Maroon">Uf</font> is <a href="card_fil.html#V1" target="_self">uniform</a> &amp; <font color="Maroon">Uf</font> is <a href="card_fil.html#V3" target="_self">being_ultrafilter</a> )
 ;<br/>

<b>thus </b><a NAME="E2:36"/>
 <a href="card_fil.html#K4" target="_self">Frechet_Filter</a> <font color="Maroon">X</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">Uf</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="36_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">Y</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:36_1"/><i><font color="Green">E24</font></i>: 
<font color="Maroon">Y</font> <a href="hidden.html#R2">in</a>  <a href="card_fil.html#K4" target="_self">Frechet_Filter</a> <font color="Maroon">X</font>
 ;<br/>

<a NAME="E2:36_1"/><b>then </b>
 <a href="card_1.html#K1">Card</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="card_1.html#NR2" target="_self">&lt;`</a>  <a href="card_1.html#K1">Card</a> <font color="Maroon">X</font>
 
<b>by </b><i/>;<br/>
<a NAME="E3:36_1"/><b>then </b>
 <a href="card_1.html#K1">Card</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#NR2" target="_self">&lt;&gt;</a>  <a href="card_1.html#K1">Card</a> <font color="Maroon">X</font>
 
;<br/>
<a NAME="E4:36_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">Uf</font>
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E5:36_1"/>
<font color="Maroon">Y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Uf</font>
 <b>by </b><i>, , </i>;<br/>


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


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