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<b>let </b><font color="Maroon" title="c1">L</font> be   <a href="lattices.html#NM1" title="LATTICES:NM.1">Lattice</a>;<br/><b>let </b><font color="Maroon" title="c2">p</font>, <font color="Maroon" title="c3">q</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font>;<br/>





<b>assume </b><a NAME="E1:117"/>
( <font color="Maroon" title="c1">L</font> is   <a href="lattices.html#NM8" title="LATTICES:NM.8">B_Lattice</a> &amp; <font color="Maroon" title="c2">p</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c3">q</font> )
 ;<br/>

<a NAME="E2:117"/><b>then </b>
 <a href="filter_2.html#K23" title="FILTER_2:func.23">latt</a> <font color="Maroon" title="c1">L</font>,<span class="p1"><a href="filter_2.html#K22" title="FILTER_2:func.22">[#</a><span class="default"><font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font></span><a href="filter_2.html#K22" title="FILTER_2:func.22">#]</a></span> is  <a href="lattices.html#V11" title="LATTICES:attr.11">distributive</a> <a href="lattices.html#V15" title="LATTICES:attr.15">bounded</a> <a href="lattices.html#V16" title="LATTICES:attr.16">complemented</a> <a href="lattices.html#NM1" title="LATTICES:NM.1">Lattice</a>
 
<b>by </b><i><a class="ref" href="filter_2.html#T78" target="_self" title="FILTER_2:th.78">Th78</a>, <a class="ref" href="filter_2.html#T86" target="_self" title="FILTER_2:th.86">Th86</a></i>;<br/>
<b>hence </b><a NAME="E3:117"/>
 <a href="filter_2.html#K23" title="FILTER_2:func.23">latt</a> <font color="Maroon" title="c1">L</font>,<span class="p1"><a href="filter_2.html#K22" title="FILTER_2:func.22">[#</a><span class="default"><font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font></span><a href="filter_2.html#K22" title="FILTER_2:func.22">#]</a></span> is   <a href="lattices.html#NM8" title="LATTICES:NM.8">B_Lattice</a>
 ;<br/>


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