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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/>

<a NAME="E1:77"/>
( ( <font color="Maroon" title="c1">L</font> is   <a href="lattices.html#NM7" title="LATTICES:NM.7">C_Lattice</a> implies <font color="Maroon" title="c1">L</font> <a href="lattice2.html#K1" title="LATTICE2:func.1">.:</a>  is   <a href="lattices.html#NM7" title="LATTICES:NM.7">C_Lattice</a> ) &amp; ( <font color="Maroon" title="c1">L</font> <a href="lattice2.html#K1" title="LATTICE2:func.1">.:</a>  is   <a href="lattices.html#NM7" title="LATTICES:NM.7">C_Lattice</a> implies <font color="Maroon" title="c1">L</font> is   <a href="lattices.html#NM7" title="LATTICES:NM.7">C_Lattice</a> ) &amp; ( <font color="Maroon" title="c1">L</font> is <a href="lattices.html#V11" title="LATTICES:attr.11">distributive</a> implies <font color="Maroon" title="c1">L</font> <a href="lattice2.html#K1" title="LATTICE2:func.1">.:</a>  is <a href="lattices.html#V11" title="LATTICES:attr.11">distributive</a> ) &amp; ( <font color="Maroon" title="c1">L</font> <a href="lattice2.html#K1" title="LATTICE2:func.1">.:</a>  is <a href="lattices.html#V11" title="LATTICES:attr.11">distributive</a> implies <font color="Maroon" title="c1">L</font> is <a href="lattices.html#V11" title="LATTICES:attr.11">distributive</a> ) &amp; ( <font color="Maroon" title="c1">L</font> is   <a href="lattices.html#NM7" title="LATTICES:NM.7">C_Lattice</a> &amp; <font color="Maroon" title="c1">L</font> is <a href="lattices.html#V11" title="LATTICES:attr.11">distributive</a> implies <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="c1">L</font> is   <a href="lattices.html#NM8" title="LATTICES:NM.8">B_Lattice</a> implies ( <font color="Maroon" title="c1">L</font> is   <a href="lattices.html#NM7" title="LATTICES:NM.7">C_Lattice</a> &amp; <font color="Maroon" title="c1">L</font> is <a href="lattices.html#V11" title="LATTICES:attr.11">distributive</a> ) ) &amp; ( <font color="Maroon" title="c1">L</font> <a href="lattice2.html#K1" title="LATTICE2:func.1">.:</a>  is   <a href="lattices.html#NM7" title="LATTICES:NM.7">C_Lattice</a> &amp; <font color="Maroon" title="c1">L</font> <a href="lattice2.html#K1" title="LATTICE2:func.1">.:</a>  is <a href="lattices.html#V11" title="LATTICES:attr.11">distributive</a> implies <font color="Maroon" title="c1">L</font> <a href="lattice2.html#K1" title="LATTICE2:func.1">.:</a>  is   <a href="lattices.html#NM8" title="LATTICES:NM.8">B_Lattice</a> ) &amp; ( <font color="Maroon" title="c1">L</font> <a href="lattice2.html#K1" title="LATTICE2:func.1">.:</a>  is   <a href="lattices.html#NM8" title="LATTICES:NM.8">B_Lattice</a> implies ( <font color="Maroon" title="c1">L</font> <a href="lattice2.html#K1" title="LATTICE2:func.1">.:</a>  is   <a href="lattices.html#NM7" title="LATTICES:NM.7">C_Lattice</a> &amp; <font color="Maroon" title="c1">L</font> <a href="lattice2.html#K1" title="LATTICE2:func.1">.:</a>  is <a href="lattices.html#V11" title="LATTICES:attr.11">distributive</a> ) ) )
 
<b>by </b><i><a class="ref" href="filter_2.html#T53" target="_self" title="FILTER_2:th.53">Th53</a>, <a class="ref" href="lattice2.html#T65" title="LATTICE2:th.65">LATTICE2:65</a>, <a class="ref" href="lattices.html#D20" title="LATTICES:def.20">LATTICES:def 20</a></i>;<br/>
<b>hence </b><a NAME="E2:77"/>
( <font color="Maroon" title="c1">L</font> is   <a href="lattices.html#NM8" title="LATTICES:NM.8">B_Lattice</a> iff <font color="Maroon" title="c1">L</font> <a href="lattice2.html#K1" title="LATTICE2:func.1">.:</a>  is   <a href="lattices.html#NM8" title="LATTICES:NM.8">B_Lattice</a> )
 ;<br/>


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