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<b>let </b><font color="Maroon">I</font> be   <a href="filter_0.html#NM2">I_Lattice</a>;<br/><b>let </b><font color="Maroon">FI</font> be    <a href="filter_0.html#M1">Filter</a> of <font color="Maroon">I</font>;<br/><b>let </b><font color="Maroon">i</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">I</font>;<br/><b>let </b><font color="Maroon">j</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">I</font>;<br/>







<a NAME="E1:81"/>
( ( <font color="Maroon">i</font> <a href="hidden.html#R2">in</a>  <a href="eqrel_1.html#K7">Class</a> <span class="p1">(<span class="default"><a href="filter_0.html#K11">equivalence_wrt</a> <font color="Maroon">FI</font></span>)</span>,<font color="Maroon">j</font> implies <span class="p1"><a href="filter_1.html#K9" target="_self">[</a><span class="default"><font color="Maroon">i</font>,<font color="Maroon">j</font></span><a href="filter_1.html#K9" target="_self">]</a></span> <a href="hidden.html#R2">in</a>  <a href="filter_0.html#K11">equivalence_wrt</a> <font color="Maroon">FI</font> ) &amp; ( <span class="p1"><a href="filter_1.html#K9" target="_self">[</a><span class="default"><font color="Maroon">i</font>,<font color="Maroon">j</font></span><a href="filter_1.html#K9" target="_self">]</a></span> <a href="hidden.html#R2">in</a>  <a href="filter_0.html#K11">equivalence_wrt</a> <font color="Maroon">FI</font> implies <font color="Maroon">i</font> <a href="hidden.html#R2">in</a>  <a href="eqrel_1.html#K7">Class</a> <span class="p1">(<span class="default"><a href="filter_0.html#K11">equivalence_wrt</a> <font color="Maroon">FI</font></span>)</span>,<font color="Maroon">j</font> ) &amp; ( <span class="p1"><a href="filter_1.html#K9" target="_self">[</a><span class="default"><font color="Maroon">i</font>,<font color="Maroon">j</font></span><a href="filter_1.html#K9" target="_self">]</a></span> <a href="hidden.html#R2">in</a>  <a href="filter_0.html#K11">equivalence_wrt</a> <font color="Maroon">FI</font> implies <font color="Maroon">i</font> <a href="filter_0.html#K9">&lt;=&gt;</a> <font color="Maroon">j</font> <a href="hidden.html#R2">in</a> <font color="Maroon">FI</font> ) &amp; ( <font color="Maroon">i</font> <a href="filter_0.html#K9">&lt;=&gt;</a> <font color="Maroon">j</font> <a href="hidden.html#R2">in</a> <font color="Maroon">FI</font> implies <span class="p1"><a href="filter_1.html#K9" target="_self">[</a><span class="default"><font color="Maroon">i</font>,<font color="Maroon">j</font></span><a href="filter_1.html#K9" target="_self">]</a></span> <a href="hidden.html#R2">in</a>  <a href="filter_0.html#K11">equivalence_wrt</a> <font color="Maroon">FI</font> ) )
 
<b>by </b><i><a class="ref" href="eqrel_1.html#T27">EQREL_1:27</a>, <a class="ref" href="filter_0.html#D12">FILTER_0:def 12</a></i>;<br/>
<b>hence </b><a NAME="E2:81"/>
( <font color="Maroon">i</font> <a href="hidden.html#R2">in</a>  <a href="eqrel_1.html#K7">Class</a> <span class="p1">(<span class="default"><a href="filter_0.html#K11">equivalence_wrt</a> <font color="Maroon">FI</font></span>)</span>,<font color="Maroon">j</font> iff <font color="Maroon">i</font> <a href="filter_0.html#K9">&lt;=&gt;</a> <font color="Maroon">j</font> <a href="hidden.html#R2">in</a> <font color="Maroon">FI</font> )
 ;<br/>


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