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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">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="E1:35"/><i><font color="Green">E22</font></i>: 
 <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">F</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>; <i><font color="Red">:: according to </font></i><a class="ref" href="card_fil.html#D5" target="_self">CARD_FIL:def 5</a><br/>

<b>assume </b><a NAME="E2:35"/>
<font color="Maroon">Y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F</font>
 ;<br/>

<a NAME="E3:35"/><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>  <a href="card_fil.html#K4" target="_self">Frechet_Filter</a> <font color="Maroon">X</font>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E4:35"/><b>then </b><i><font color="Green">E24</font></i>: 
not  <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> <span class="p2">(<span class="default"><font color="Maroon">X</font> <a href="subset_1.html#K6">\</a> <font color="Maroon">Y</font></span>)</span></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>
 
;<br/>
<font color="Maroon">X</font> <a href="subset_1.html#K6">\</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> = 
<font color="Maroon">X</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">Y</font>
<b>by </b><i><a class="ref" href="xboole_1.html#T48">XBOOLE_1:48</a></i>
<br/>.= 
<font color="Maroon">Y</font>
<b>by </b><i><a class="ref" href="xboole_1.html#T28">XBOOLE_1:28</a></i>
;<br/>
<a NAME="E6:35"/><b>then </b><i><font color="Green">E25</font></i>: 
 <a href="card_1.html#K1">Card</a> <font color="Maroon">X</font> <a href="card_1.html#NR1" target="_self">&lt;=`</a>  <a href="card_1.html#K1">Card</a> <font color="Maroon">Y</font>
 
<b>by </b><i>, <a class="ref" href="card_1.html#T14">CARD_1:14</a></i>;<br/>
<a NAME="E7:35"/>
 <a href="card_1.html#K1">Card</a> <font color="Maroon">Y</font> <a href="card_1.html#NR1" target="_self">&lt;=`</a>  <a href="card_1.html#K1">Card</a> <font color="Maroon">X</font>
 
<b>by </b><i><a class="ref" href="card_1.html#T27">CARD_1:27</a></i>;<br/>
<b>hence </b><a NAME="E8:35"/>
 <a href="card_1.html#K1">Card</a> <font color="Maroon">Y</font> <a href="hidden.html#R1">=</a>  <a href="card_1.html#K1">Card</a> <font color="Maroon">X</font>
 <b>by </b><i>, <a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a></i>;<br/>


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