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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="lattices.html#NM1">Lattice</a>;<br/>

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


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