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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>assume </b><a NAME="E1:42"/>
<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> is    <a href="filter_2.html#M2" target="_self">Ideal</a> of <font color="Maroon">L</font>
 ;<br/>

<a NAME="E2:42"/><b>then </b>
( <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="domain_1.html#K6">{</a><span class="default"><font color="Maroon">p</font></span><a href="domain_1.html#K6">}</a></span> is    <a href="filter_2.html#M1" target="_self">Filter</a> of <font color="Maroon">L</font> <a href="lattice2.html#K1">.:</a>  )
 
<b>by </b><i/>;<br/>
<a NAME="E3:42"/><b>then </b>
<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="filter_0.html#T14">FILTER_0:14</a></i>;<br/>
<b>hence </b><a NAME="E4:42"/>
<font color="Maroon">L</font> is <a href="lattices.html#V13">lower-bounded</a>
 <b>by </b><i><a class="ref" href="lattice2.html#T63">LATTICE2:63</a></i>;<br/>


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