<?xml version="1.0"?>
<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E12">Th19</font></span>: <a NAME="T19"><span class="comment"><font color="firebrick">:: LOPCLSET:19</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">BL</font> being   non  <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a>  <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">BL</font><br/>  for <font color="Olive" title="b4">F</font> being   <a href="filter_0.html#NM1" title="FILTER_0:NM.1">Filter</a> of <font color="Olive" title="b1">BL</font>  st <font color="Olive" title="b4">F</font> is  <a href="filter_0.html#V1" title="FILTER_0:attr.1">being_ultrafilter</a>  holds <br/>( <font color="Olive" title="b2">a</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Olive" title="b3">b</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b4">F</font> iff ( <font color="Olive" title="b2">a</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b4">F</font> or <font color="Olive" title="b3">b</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b4">F</font> ) )</div></div>
