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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="lattices.html#NM1">Lattice</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font> be    <a href="filter_0.html#M1" target="_self">Filter</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>







<a NAME="E1:93"/>
( ( <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="filter_0.html#R1" target="_self">are_equivalence_wrt</a> <font color="Maroon">c<sub>4</sub></font> implies <font color="Maroon">c<sub>2</sub></font> <a href="filter_0.html#K9" target="_self">&lt;=&gt;</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>4</sub></font> ) &amp; ( <font color="Maroon">c<sub>2</sub></font> <a href="filter_0.html#K9" target="_self">&lt;=&gt;</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>4</sub></font> implies <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="filter_0.html#R1" target="_self">are_equivalence_wrt</a> <font color="Maroon">c<sub>4</sub></font> ) &amp; ( <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="domain_1.html#K1">]</a></span> <a href="hidden.html#R2">in</a>  <a href="filter_0.html#K10" target="_self">equivalence_wrt</a> <font color="Maroon">c<sub>4</sub></font> implies <font color="Maroon">c<sub>2</sub></font> <a href="filter_0.html#K9" target="_self">&lt;=&gt;</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>4</sub></font> ) &amp; ( <font color="Maroon">c<sub>2</sub></font> <a href="filter_0.html#K9" target="_self">&lt;=&gt;</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>4</sub></font> implies <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="domain_1.html#K1">]</a></span> <a href="hidden.html#R2">in</a>  <a href="filter_0.html#K10" target="_self">equivalence_wrt</a> <font color="Maroon">c<sub>4</sub></font> ) )
 
<b>by </b><i><a class="ref" href="filter_0.html#D12" target="_self">Def12</a>, <a class="ref" href="filter_0.html#D13" target="_self">Def13</a></i>;<br/>
<b>hence </b><a NAME="E2:93"/>
( <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="filter_0.html#R1" target="_self">are_equivalence_wrt</a> <font color="Maroon">c<sub>4</sub></font> iff <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="domain_1.html#K1">]</a></span> <a href="hidden.html#R2">in</a>  <a href="filter_0.html#K10" target="_self">equivalence_wrt</a> <font color="Maroon">c<sub>4</sub></font> )
 ;<br/>


</div>
