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<b>let </b><font color="Maroon">L</font> be   <a href="lattices.html#NM1">Lattice</a>;<br/>

<b>assume </b><a NAME="E1:49"/>
<font color="Maroon">L</font> is <a href="lattices.html#V14">upper-bounded</a>
 ;<br/>

<a NAME="E2:49"/><b>then </b>
( <font color="Maroon">L</font> <a href="lattice2.html#K1">.:</a>  is <a href="lattices.html#V13">lower-bounded</a> &amp;  <a href="lattices.html#K6">Top</a> <font color="Maroon">L</font> <a href="hidden.html#R1">=</a>  <a href="lattices.html#K5">Bottom</a> <span class="p1">(<span class="default"><font color="Maroon">L</font> <a href="lattice2.html#K1">.:</a> </span>)</span> )
 
<b>by </b><i><a class="ref" href="lattice2.html#T64">LATTICE2:64</a>, <a class="ref" href="lattice2.html#T79">LATTICE2:79</a></i>;<br/>
<a NAME="E3:49"/><b>then </b>
( <span class="p1"><a href="filter_2.html#K1" target="_self">&lt;.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">L</font> <a href="lattice2.html#K1">.:</a> </span>)</span></span><a href="filter_2.html#K1" target="_self">.)</a></span> <a href="filter_2.html#R1" target="_self">=</a> <span class="p1"><a href="filter_2.html#K2" target="_self">&lt;.</a><span class="default"><span class="p2">(<span class="default"><a href="lattices.html#K5">Bottom</a> <span class="p3">(<span class="default"><font color="Maroon">L</font> <a href="lattice2.html#K1">.:</a> </span>)</span></span>)</span></span><a href="filter_2.html#K2" target="_self">.)</a></span> &amp; <span class="p1"><a href="filter_2.html#K1" target="_self">&lt;.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">L</font> <a href="lattice2.html#K1">.:</a> </span>)</span></span><a href="filter_2.html#K1" target="_self">.)</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">L</font> <a href="lattice2.html#K1">.:</a> ) &amp; <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">L</font> <a href="lattice2.html#K1">.:</a> ) <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">L</font>) &amp; <span class="p1"><a href="filter_2.html#K17" target="_self">(.</a><span class="default"><font color="Maroon">L</font></span><a href="filter_2.html#K17" target="_self">.&gt;</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">L</font>) &amp;  <a href="lattices.html#K5">Bottom</a> <span class="p1">(<span class="default"><font color="Maroon">L</font> <a href="lattice2.html#K1">.:</a> </span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="lattices.html#K6">Top</a> <font color="Maroon">L</font></span>)</span> <a href="filter_2.html#K5" target="_self">.:</a>  )
 
<b>by </b><i><a class="ref" href="filter_0.html#T20">FILTER_0:20</a></i>;<br/>
<b>hence </b><a NAME="E4:49"/>
<span class="p1"><a href="filter_2.html#K17" target="_self">(.</a><span class="default"><font color="Maroon">L</font></span><a href="filter_2.html#K17" 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"><span class="p2">(<span class="default"><a href="lattices.html#K6">Top</a> <font color="Maroon">L</font></span>)</span></span><a href="filter_2.html#K18" target="_self">.&gt;</a></span>
 <b>by </b><i/>;<br/>


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