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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>let </b><font color="Maroon">q</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>;<br/>





<b>assume </b><a NAME="E1:117"/>
( <font color="Maroon">L</font> is   <a href="lattices.html#NM8">B_Lattice</a> &amp; <font color="Maroon">p</font> <a href="lattices.html#R3">[=</a> <font color="Maroon">q</font> )
 ;<br/>

<a NAME="E2:117"/><b>then </b>
 <a href="filter_2.html#K23" target="_self">latt</a> <font color="Maroon">L</font>,<span class="p1"><a href="filter_2.html#K22" target="_self">[#</a><span class="default"><font color="Maroon">p</font>,<font color="Maroon">q</font></span><a href="filter_2.html#K22" target="_self">#]</a></span> is  <a href="lattices.html#V11">distributive</a> <a href="lattices.html#V15">bounded</a> <a href="lattices.html#V16">complemented</a> <a href="lattices.html#NM1">Lattice</a>
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E3:117"/>
 <a href="filter_2.html#K23" target="_self">latt</a> <font color="Maroon">L</font>,<span class="p1"><a href="filter_2.html#K22" target="_self">[#</a><span class="default"><font color="Maroon">p</font>,<font color="Maroon">q</font></span><a href="filter_2.html#K22" target="_self">#]</a></span> is   <a href="lattices.html#NM8">B_Lattice</a>
 ;<br/>


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