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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">I</font> be    <a href="filter_2.html#M2" target="_self">Ideal</a> of <font color="Maroon">L</font>;<br/>



<b>assume </b><a NAME="E1:40"/>
<font color="Maroon">L</font> is <a href="lattices.html#V13">lower-bounded</a>
 ;<br/>

<a NAME="E2:40"/><b>then </b>
(  <a href="lattices.html#K6">Top</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>  <a href="lattices.html#K5">Bottom</a> <font color="Maroon">L</font> &amp; <font color="Maroon">L</font> <a href="lattice2.html#K1">.:</a>  is <a href="lattices.html#V14">upper-bounded</a> )
 
<b>by </b><i><a class="ref" href="lattice2.html#T63">LATTICE2:63</a>, <a class="ref" href="lattice2.html#T78">LATTICE2:78</a></i>;<br/>
<a NAME="E3:40"/><b>then </b>
 <a href="lattices.html#K5">Bottom</a> <font color="Maroon">L</font> <a href="hidden.html#R2">in</a> <font color="Maroon">I</font> <a href="filter_2.html#K15" target="_self">.:</a> 
 
<b>by </b><i><a class="ref" href="filter_0.html#T12">FILTER_0:12</a></i>;<br/>
<b>hence </b><a NAME="E4:40"/>
 <a href="lattices.html#K5">Bottom</a> <font color="Maroon">L</font> <a href="hidden.html#R2">in</a> <font color="Maroon">I</font>
 ;<br/>


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