<?xml version="1.0"?>
<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E42">Th38</font></span>: <a NAME="T46"><span class="comment"><font color="firebrick">:: CARDFIL4:46</font></span><br/></a><div class="add">( <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>,<a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1"> { <span class="default"> <span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><a href="ordinal1.html#K5" title="ORDINAL1:func.5">0</a>,<font color="Olive" title="b1">n</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> where <font color="Olive" title="b1">n</font> is   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> : verum </span> } </span>  <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1"><a href="cardfil4.html#K2" title="CARDFIL4:func.2">&lt;.</a><span class="default"><span class="p2">(<span class="default"><a href="card_fil.html#K4" title="CARD_FIL:func.4">Frechet_Filter</a> <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a></span>)</span>,<span class="p2">(<span class="default"><a href="card_fil.html#K4" title="CARD_FIL:func.4">Frechet_Filter</a> <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a></span>)</span></span><a href="cardfil4.html#K2" title="CARDFIL4:func.2">.)</a></span> &amp;  not <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>,<a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1"> { <span class="default"> <span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><a href="ordinal1.html#K5" title="ORDINAL1:func.5">0</a>,<font color="Olive" title="b1">n</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> where <font color="Olive" title="b1">n</font> is   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> : verum </span> } </span>  <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="card_fil.html#K4" title="CARD_FIL:func.4">Frechet_Filter</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>,<a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> )</div></div>
