<?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  non <a href="xboole_0.html#V1">empty</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>





<a NAME="E1:72"/>
( <span class="p1"><a href="filter_2.html#K19" target="_self">(.</a><span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="filter_2.html#K19" target="_self">(.</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="filter_2.html#K19" target="_self">.&gt;</a></span> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span><a href="filter_2.html#K19" target="_self">.&gt;</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="filter_2.html#K3" target="_self">&lt;.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4"><a href="filter_2.html#K19" target="_self">(.</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="filter_2.html#K19" target="_self">.&gt;</a></span> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="filter_2.html#K7" target="_self">.:</a> </span>)</span></span><a href="filter_2.html#K3" target="_self">.)</a></span> &amp; <span class="p1"><a href="filter_2.html#K19" target="_self">(.</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="filter_2.html#K19" target="_self">.&gt;</a></span> <a href="hidden.html#R1">=</a> <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">c<sub>2</sub></font> <a href="filter_2.html#K7" target="_self">.:</a> </span>)</span></span><a href="filter_2.html#K3" target="_self">.)</a></span> &amp; <span class="p1"><a href="filter_2.html#K19" target="_self">(.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K4">\/</a> <span class="p3"><a href="filter_2.html#K19" target="_self">(.</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="filter_2.html#K19" target="_self">.&gt;</a></span></span>)</span></span><a href="filter_2.html#K19" target="_self">.&gt;</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="filter_2.html#K3" target="_self">&lt;.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K4">\/</a> <span class="p4"><a href="filter_2.html#K19" target="_self">(.</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="filter_2.html#K19" target="_self">.&gt;</a></span></span>)</span> <a href="filter_2.html#K7" target="_self">.:</a> </span>)</span></span><a href="filter_2.html#K3" target="_self">.)</a></span> &amp; <span class="p1"><a href="filter_2.html#K19" target="_self">(.</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="filter_2.html#K19" target="_self">.&gt;</a></span> <a href="hidden.html#R1">=</a> <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">c<sub>3</sub></font> <a href="filter_2.html#K7" target="_self">.:</a> </span>)</span></span><a href="filter_2.html#K3" target="_self">.)</a></span> &amp; <span class="p1"><a href="filter_2.html#K19" target="_self">(.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span><a href="filter_2.html#K19" target="_self">.&gt;</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="filter_2.html#K3" target="_self">&lt;.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="filter_2.html#K7" target="_self">.:</a> </span>)</span></span><a href="filter_2.html#K3" target="_self">.)</a></span> &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K4">\/</a> <span class="p2"><a href="filter_2.html#K19" target="_self">(.</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="filter_2.html#K19" target="_self">.&gt;</a></span></span>)</span> <a href="filter_2.html#K7" target="_self">.:</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K4">\/</a> <span class="p1"><a href="filter_2.html#K19" target="_self">(.</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="filter_2.html#K19" target="_self">.&gt;</a></span> &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="filter_2.html#K7" target="_self">.:</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="filter_2.html#K7" target="_self">.:</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="filter_2.html#K7" target="_self">.:</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <span class="p1">(<span class="default"><span class="p2"><a href="filter_2.html#K19" target="_self">(.</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="filter_2.html#K19" target="_self">.&gt;</a></span> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="filter_2.html#K7" target="_self">.:</a>  <a href="hidden.html#R1">=</a> <span class="p1"><a href="filter_2.html#K19" target="_self">(.</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="filter_2.html#K19" target="_self">.&gt;</a></span> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>3</sub></font> &amp; <span class="p1"><a href="filter_2.html#K19" target="_self">(.</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="filter_2.html#K19" target="_self">.&gt;</a></span> <a href="filter_2.html#K15" target="_self">.:</a>  <a href="hidden.html#R1">=</a> <span class="p1"><a href="filter_2.html#K19" target="_self">(.</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="filter_2.html#K19" target="_self">.&gt;</a></span> &amp; <span class="p1"><a href="filter_2.html#K19" target="_self">(.</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="filter_2.html#K19" target="_self">.&gt;</a></span> <a href="filter_2.html#K15" target="_self">.:</a>  <a href="hidden.html#R1">=</a> <span class="p1"><a href="filter_2.html#K19" target="_self">(.</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="filter_2.html#K19" target="_self">.&gt;</a></span> )
 
<b>by </b><i><a class="ref" href="filter_2.html#T37" target="_self">Th37</a></i>;<br/>
<b>hence </b><a NAME="E2:72"/>
( <span class="p1"><a href="filter_2.html#K19" target="_self">(.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></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#K19" target="_self">(.</a><span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="filter_2.html#K19" target="_self">(.</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="filter_2.html#K19" target="_self">.&gt;</a></span> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span><a href="filter_2.html#K19" target="_self">.&gt;</a></span> &amp; <span class="p1"><a href="filter_2.html#K19" target="_self">(.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></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#K19" target="_self">(.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K4">\/</a> <span class="p3"><a href="filter_2.html#K19" target="_self">(.</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="filter_2.html#K19" target="_self">.&gt;</a></span></span>)</span></span><a href="filter_2.html#K19" target="_self">.&gt;</a></span> )
 <b>by </b><i><a class="ref" href="filter_0.html#T47">FILTER_0:47</a></i>;<br/>


</div>
