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<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> 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="c3">D</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">L</font>;<br/>





<a NAME="E1:61"/>
( <font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">p</font> <a href="filter_2.html#K5" title="FILTER_2:func.5">.:</a>  &amp; <span class="p1"><a href="filter_2.html#K2" title="FILTER_2:func.2">&lt;.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="filter_2.html#K5" title="FILTER_2:func.5">.:</a> </span>)</span></span><a href="filter_2.html#K2" title="FILTER_2:func.2">.)</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="filter_2.html#K18" title="FILTER_2:func.18">(.</a><span class="default"><font color="Maroon" title="c2">p</font></span><a href="filter_2.html#K18" title="FILTER_2:func.18">.&gt;</a></span> &amp; <font color="Maroon" title="c3">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">D</font> <a href="filter_2.html#K7" title="FILTER_2:func.7">.:</a>  &amp; <span class="p1"><a href="filter_2.html#K3" title="FILTER_2:func.3">&lt;.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">D</font> <a href="filter_2.html#K7" title="FILTER_2:func.7">.:</a> </span>)</span></span><a href="filter_2.html#K3" title="FILTER_2:func.3">.)</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="filter_2.html#K19" title="FILTER_2:func.19">(.</a><span class="default"><font color="Maroon" title="c3">D</font></span><a href="filter_2.html#K19" title="FILTER_2:func.19">.&gt;</a></span> )
 
<b>by </b><i><a class="ref" href="filter_2.html#T30" target="_self" title="FILTER_2:th.30">Th30</a>, <a class="ref" href="filter_2.html#T37" target="_self" title="FILTER_2:th.37">Th37</a></i>;<br/>
<b>hence </b><a NAME="E2:61"/>
( <font color="Maroon" title="c3">D</font> <a href="filter_2.html#R1" title="FILTER_2:pred.1">=</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c2">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> implies <span class="p1"><a href="filter_2.html#K19" title="FILTER_2:func.19">(.</a><span class="default"><font color="Maroon" title="c3">D</font></span><a href="filter_2.html#K19" title="FILTER_2:func.19">.&gt;</a></span> <a href="filter_2.html#R1" title="FILTER_2:pred.1">=</a> <span class="p1"><a href="filter_2.html#K18" title="FILTER_2:func.18">(.</a><span class="default"><font color="Maroon" title="c2">p</font></span><a href="filter_2.html#K18" title="FILTER_2:func.18">.&gt;</a></span> )
 <b>by </b><i><a class="ref" href="filter_0.html#T30" title="FILTER_0:th.30">FILTER_0:30</a></i>;<br/>


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