<?xml version="1.0"?>
<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E45">Th82</font></span>: <a NAME="T82"><span class="comment"><font color="firebrick">:: FILTER_2:82</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">L</font> being   <a href="lattices.html#NM1" title="LATTICES:NM.1">Lattice</a><br/>  for <font color="Olive" title="b2">p</font>, <font color="Olive" title="b3">q</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">L</font>  st <font color="Olive" title="b2">p</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Olive" title="b3">q</font> holds <br/>(  <a href="filter_2.html#K10" title="FILTER_2:func.10">latt</a> (<font color="Olive" title="b1">L</font>,<span class="p1"><a href="filter_2.html#K9" title="FILTER_2:func.9">[#</a><span class="default"><font color="Olive" title="b2">p</font>,<font color="Olive" title="b3">q</font></span><a href="filter_2.html#K9" title="FILTER_2:func.9">#]</a></span>) is  <a href="lattices.html#V15" title="LATTICES:attr.15">bounded</a>  &amp;  <a href="lattices.html#K6" title="LATTICES:func.6">Top</a> <span class="p1">(<span class="default"><a href="filter_2.html#K10" title="FILTER_2:func.10">latt</a> (<font color="Olive" title="b1">L</font>,<span class="p2"><a href="filter_2.html#K9" title="FILTER_2:func.9">[#</a><span class="default"><font color="Olive" title="b2">p</font>,<font color="Olive" title="b3">q</font></span><a href="filter_2.html#K9" title="FILTER_2:func.9">#]</a></span>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">q</font> &amp;  <a href="lattices.html#K5" title="LATTICES:func.5">Bottom</a> <span class="p1">(<span class="default"><a href="filter_2.html#K10" title="FILTER_2:func.10">latt</a> (<font color="Olive" title="b1">L</font>,<span class="p2"><a href="filter_2.html#K9" title="FILTER_2:func.9">[#</a><span class="default"><font color="Olive" title="b2">p</font>,<font color="Olive" title="b3">q</font></span><a href="filter_2.html#K9" title="FILTER_2:func.9">#]</a></span>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">p</font> )</div></div>
