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<b>let </b><font color="Maroon" title="c1">X</font> be  <a href="finset_1.html#NV2" title="FINSET_1:NV.2">infinite</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c2">Y</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font>;<br/>



<a NAME="E1:34"/>
( <font color="Maroon" title="c2">Y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="card_fil.html#K5" title="CARD_FIL:func.5">Frechet_Ideal</a> <font color="Maroon" title="c1">X</font> iff <font color="Maroon" title="c2">Y</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="card_fil.html#K4" title="CARD_FIL:func.4">Frechet_Filter</a> <font color="Maroon" title="c1">X</font> )
 
<b>by </b><i><a class="ref" href="setfam_1.html#D8" title="SETFAM_1:def.8">SETFAM_1:def 8</a></i>;<br/>
<a NAME="E2:34"/><b>then </b>
( <font color="Maroon" title="c2">Y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="card_fil.html#K5" title="CARD_FIL:func.5">Frechet_Ideal</a> <font color="Maroon" title="c1">X</font> iff  <a href="card_1.html#K1" title="CARD_1:func.1">Card</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">Y</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> </span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> </span>)</span> <a href="card_1.html#NR2" title="CARD_1:NR.2">&lt;`</a>  <a href="card_1.html#K1" title="CARD_1:func.1">Card</a> <font color="Maroon" title="c1">X</font> )
 
<b>by </b><i><a class="ref" href="card_fil.html#T18" target="_self" title="CARD_FIL:th.18">Th18</a></i>;<br/>
<b>hence </b><a NAME="E3:34"/>
( <font color="Maroon" title="c2">Y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="card_fil.html#K5" title="CARD_FIL:func.5">Frechet_Ideal</a> <font color="Maroon" title="c1">X</font> iff  <a href="card_1.html#K1" title="CARD_1:func.1">Card</a> <font color="Maroon" title="c2">Y</font> <a href="card_1.html#NR2" title="CARD_1:NR.2">&lt;`</a>  <a href="card_1.html#K1" title="CARD_1:func.1">Card</a> <font color="Maroon" title="c1">X</font> )
 ;<br/>


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