<?xml version="1.0"?>
<div><span class="kw">theorem </span><a NAME="T47"><span class="comment"><font color="firebrick">:: FILTER_0:47</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">B</font> being   <a href="lattices.html#NM8" title="LATTICES:NM.8">B_Lattice</a><br/>  for <font color="Olive" title="b2">a</font>, <font color="Olive" title="b3">b</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">B</font>  st <font color="Olive" title="b2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b3">b</font> holds <br/> ex <font color="Olive" title="b4">FB</font> being   <a href="filter_0.html#NM1" title="FILTER_0:NM.1">Filter</a> of <font color="Olive" title="b1">B</font> st <br/>( <font color="Olive" title="b4">FB</font> is  <a href="filter_0.html#V1" title="FILTER_0:attr.1">being_ultrafilter</a>  &amp; ( ( <font color="Olive" title="b2">a</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b4">FB</font> &amp;  not <font color="Olive" title="b3">b</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b4">FB</font> ) or (  not <font color="Olive" title="b2">a</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b4">FB</font> &amp; <font color="Olive" title="b3">b</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b4">FB</font> ) ) )</div></div>
