<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon" title="c1">L</font> be   <a href="lattices.html#NM1" title="LATTICES:NM.1">Lattice</a>;<br/><b>let </b><font color="Maroon" title="c2">p</font>, <font color="Maroon" title="c3">q</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font>;<br/><b>let </b><font color="Maroon" title="c4">F</font> be    <a href="filter_0.html#M1" title="FILTER_0:mode.1">Filter</a> of <font color="Maroon" title="c1">L</font>;<br/>







<a NAME="E1:93"/>
( ( <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font> <a href="filter_0.html#R1" title="FILTER_0:pred.1">are_equivalence_wrt</a> <font color="Maroon" title="c4">F</font> implies <font color="Maroon" title="c2">p</font> <a href="filter_0.html#K9" title="FILTER_0:func.9">&lt;=&gt;</a> <font color="Maroon" title="c3">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">F</font> ) &amp; ( <font color="Maroon" title="c2">p</font> <a href="filter_0.html#K9" title="FILTER_0:func.9">&lt;=&gt;</a> <font color="Maroon" title="c3">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">F</font> implies <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font> <a href="filter_0.html#R1" title="FILTER_0:pred.1">are_equivalence_wrt</a> <font color="Maroon" title="c4">F</font> ) &amp; ( <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="filter_0.html#K10" title="FILTER_0:func.10">equivalence_wrt</a> <font color="Maroon" title="c4">F</font> implies <font color="Maroon" title="c2">p</font> <a href="filter_0.html#K9" title="FILTER_0:func.9">&lt;=&gt;</a> <font color="Maroon" title="c3">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">F</font> ) &amp; ( <font color="Maroon" title="c2">p</font> <a href="filter_0.html#K9" title="FILTER_0:func.9">&lt;=&gt;</a> <font color="Maroon" title="c3">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">F</font> implies <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="filter_0.html#K10" title="FILTER_0:func.10">equivalence_wrt</a> <font color="Maroon" title="c4">F</font> ) )
 
<b>by </b><i><a class="ref" href="filter_0.html#D12" target="_self" title="FILTER_0:def.12">Def12</a>, <a class="ref" href="filter_0.html#D13" target="_self" title="FILTER_0:def.13">Def13</a></i>;<br/>
<b>hence </b><a NAME="E2:93"/>
( <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font> <a href="filter_0.html#R1" title="FILTER_0:pred.1">are_equivalence_wrt</a> <font color="Maroon" title="c4">F</font> iff <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="filter_0.html#K10" title="FILTER_0:func.10">equivalence_wrt</a> <font color="Maroon" title="c4">F</font> )
 ;<br/>


</div>
