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<b>let </b><font color="Maroon">L</font> be   <a href="lattices.html#NM1">Lattice</a>;<br/><b>let </b><font color="Maroon">p</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>;<br/><b>let </b><font color="Maroon">D</font> be  non <a href="xboole_0.html#V1">empty</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">L</font>;<br/>





<a NAME="E1:61"/>
( <font color="Maroon">p</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p</font> <a href="filter_2.html#K5" target="_self">.:</a>  &amp; <span class="p1"><a href="filter_2.html#K2" target="_self">&lt;.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">p</font> <a href="filter_2.html#K5" target="_self">.:</a> </span>)</span></span><a href="filter_2.html#K2" target="_self">.)</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="filter_2.html#K18" target="_self">(.</a><span class="default"><font color="Maroon">p</font></span><a href="filter_2.html#K18" target="_self">.&gt;</a></span> &amp; <font color="Maroon">D</font> <a href="hidden.html#R1">=</a> <font color="Maroon">D</font> <a href="filter_2.html#K7" target="_self">.:</a>  &amp; <span class="p1"><a href="filter_2.html#K3" target="_self">&lt;.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">D</font> <a href="filter_2.html#K7" target="_self">.:</a> </span>)</span></span><a href="filter_2.html#K3" target="_self">.)</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="filter_2.html#K19" target="_self">(.</a><span class="default"><font color="Maroon">D</font></span><a href="filter_2.html#K19" target="_self">.&gt;</a></span> )
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E2:61"/>
( <font color="Maroon">D</font> <a href="filter_2.html#R1" target="_self">=</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">p</font></span><a href="domain_1.html#K6">}</a></span> implies <span class="p1"><a href="filter_2.html#K19" target="_self">(.</a><span class="default"><font color="Maroon">D</font></span><a href="filter_2.html#K19" target="_self">.&gt;</a></span> <a href="filter_2.html#R1" target="_self">=</a> <span class="p1"><a href="filter_2.html#K18" target="_self">(.</a><span class="default"><font color="Maroon">p</font></span><a href="filter_2.html#K18" target="_self">.&gt;</a></span> )
 <b>by </b><i><a class="ref" href="filter_0.html#T30">FILTER_0:30</a></i>;<br/>


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