<?xml version="1.0"?>
<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E54">Th59</font></span>: <a NAME="T59"><span class="comment"><font color="firebrick">:: FILTER_1:59</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">I</font> being   <a href="filter_0.html#NM2" title="FILTER_0:NM.2">I_Lattice</a><br/>  for <font color="Olive" title="b2">FI</font> being   <a href="filter_0.html#NM1" title="FILTER_0:NM.1">Filter</a> of <font color="Olive" title="b1">I</font><br/>  for <font color="Olive" title="b3">i</font>, <font color="Olive" title="b4">j</font>, <font color="Olive" title="b5">k</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">I</font>  st <font color="Olive" title="b3">i</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<span class="p1">(<span class="default"><a href="filter_0.html#K9" title="FILTER_0:func.9">equivalence_wrt</a> <font color="Olive" title="b2">FI</font></span>)</span>,<font color="Olive" title="b5">k</font>) &amp; <font color="Olive" title="b4">j</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<span class="p1">(<span class="default"><a href="filter_0.html#K9" title="FILTER_0:func.9">equivalence_wrt</a> <font color="Olive" title="b2">FI</font></span>)</span>,<font color="Olive" title="b5">k</font>) holds <br/>( <font color="Olive" title="b3">i</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Olive" title="b4">j</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<span class="p1">(<span class="default"><a href="filter_0.html#K9" title="FILTER_0:func.9">equivalence_wrt</a> <font color="Olive" title="b2">FI</font></span>)</span>,<font color="Olive" title="b5">k</font>) &amp; <font color="Olive" title="b3">i</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Olive" title="b4">j</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<span class="p1">(<span class="default"><a href="filter_0.html#K9" title="FILTER_0:func.9">equivalence_wrt</a> <font color="Olive" title="b2">FI</font></span>)</span>,<font color="Olive" title="b5">k</font>) )</div></div>
