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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E35">Th31</font></span>: <a NAME="T38"><span class="comment"><font color="firebrick">:: CARDFIL4:38</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">x</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <span class="p1"><a href="cardfil4.html#K1" title="CARDFIL4:func.1">[:</a><span class="default"><a href="cardfil2.html#K11" title="CARDFIL2:func.11">base_of_frechet_filter</a>,<a href="cardfil2.html#K11" title="CARDFIL2:func.11">base_of_frechet_filter</a></span><a href="cardfil4.html#K1" title="CARDFIL4:func.1">:]</a></span>  ex <font color="Olive" title="b2">i</font>, <font color="Olive" title="b3">j</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> st <font color="Olive" title="b1">x</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1"><a href="mcart_1.html#K8" title="MCART_1:func.8">[:</a><span class="default"><span class="p2">(<span class="default"><a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">Segm</a> <font color="Olive" title="b2">i</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">Segm</a> <font color="Olive" title="b3">j</font></span>)</span></span>)</span></span><a href="mcart_1.html#K8" title="MCART_1:func.8">:]</a></span></div></div>
