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<b>let </b><font color="Maroon" title="c1">L1</font>, <font color="Maroon" title="c2">L2</font> be   <a href="lattices.html#NM1" title="LATTICES:NM.1">Lattice</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( ( <font color="Maroon" title="c1">L1</font> is   <a href="lattices.html#NM8" title="LATTICES:NM.8">B_Lattice</a> &amp; <font color="Maroon" title="c2">L2</font> is   <a href="lattices.html#NM8" title="LATTICES:NM.8">B_Lattice</a> ) iff <span class="p1"><a href="filter_1.html#K7" title="FILTER_1:func.7">[:</a><span class="default"><font color="Maroon" title="c1">L1</font>,<font color="Maroon" title="c2">L2</font></span><a href="filter_1.html#K7" title="FILTER_1:func.7">:]</a></span> is   <a href="lattices.html#NM8" title="LATTICES:NM.8">B_Lattice</a> )</span><br/>



<a NAME="E1:66"/>
( ( <font color="Maroon" title="c1">L1</font> is   <a href="lattices.html#NM8" title="LATTICES:NM.8">B_Lattice</a> implies ( <font color="Maroon" title="c1">L1</font> is   <a href="lattices.html#NM7" title="LATTICES:NM.7">C_Lattice</a> &amp; <font color="Maroon" title="c1">L1</font> is   <a href="lattices.html#NM2" title="LATTICES:NM.2">D_Lattice</a> ) ) &amp; ( <font color="Maroon" title="c1">L1</font> is   <a href="lattices.html#NM7" title="LATTICES:NM.7">C_Lattice</a> &amp; <font color="Maroon" title="c1">L1</font> is   <a href="lattices.html#NM2" title="LATTICES:NM.2">D_Lattice</a> implies <font color="Maroon" title="c1">L1</font> is   <a href="lattices.html#NM8" title="LATTICES:NM.8">B_Lattice</a> ) &amp; ( <font color="Maroon" title="c2">L2</font> is   <a href="lattices.html#NM8" title="LATTICES:NM.8">B_Lattice</a> implies ( <font color="Maroon" title="c2">L2</font> is   <a href="lattices.html#NM7" title="LATTICES:NM.7">C_Lattice</a> &amp; <font color="Maroon" title="c2">L2</font> is   <a href="lattices.html#NM2" title="LATTICES:NM.2">D_Lattice</a> ) ) &amp; ( <font color="Maroon" title="c2">L2</font> is   <a href="lattices.html#NM7" title="LATTICES:NM.7">C_Lattice</a> &amp; <font color="Maroon" title="c2">L2</font> is   <a href="lattices.html#NM2" title="LATTICES:NM.2">D_Lattice</a> implies <font color="Maroon" title="c2">L2</font> is   <a href="lattices.html#NM8" title="LATTICES:NM.8">B_Lattice</a> ) &amp; ( <span class="p1"><a href="filter_1.html#K7" title="FILTER_1:func.7">[:</a><span class="default"><font color="Maroon" title="c1">L1</font>,<font color="Maroon" title="c2">L2</font></span><a href="filter_1.html#K7" title="FILTER_1:func.7">:]</a></span> is   <a href="lattices.html#NM7" title="LATTICES:NM.7">C_Lattice</a> implies ( <font color="Maroon" title="c1">L1</font> is   <a href="lattices.html#NM7" title="LATTICES:NM.7">C_Lattice</a> &amp; <font color="Maroon" title="c2">L2</font> is   <a href="lattices.html#NM7" title="LATTICES:NM.7">C_Lattice</a> ) ) &amp; ( <font color="Maroon" title="c1">L1</font> is   <a href="lattices.html#NM7" title="LATTICES:NM.7">C_Lattice</a> &amp; <font color="Maroon" title="c2">L2</font> is   <a href="lattices.html#NM7" title="LATTICES:NM.7">C_Lattice</a> implies <span class="p1"><a href="filter_1.html#K7" title="FILTER_1:func.7">[:</a><span class="default"><font color="Maroon" title="c1">L1</font>,<font color="Maroon" title="c2">L2</font></span><a href="filter_1.html#K7" title="FILTER_1:func.7">:]</a></span> is   <a href="lattices.html#NM7" title="LATTICES:NM.7">C_Lattice</a> ) &amp; ( <span class="p1"><a href="filter_1.html#K7" title="FILTER_1:func.7">[:</a><span class="default"><font color="Maroon" title="c1">L1</font>,<font color="Maroon" title="c2">L2</font></span><a href="filter_1.html#K7" title="FILTER_1:func.7">:]</a></span> is   <a href="lattices.html#NM2" title="LATTICES:NM.2">D_Lattice</a> implies ( <font color="Maroon" title="c1">L1</font> is   <a href="lattices.html#NM2" title="LATTICES:NM.2">D_Lattice</a> &amp; <font color="Maroon" title="c2">L2</font> is   <a href="lattices.html#NM2" title="LATTICES:NM.2">D_Lattice</a> ) ) &amp; ( <font color="Maroon" title="c1">L1</font> is   <a href="lattices.html#NM2" title="LATTICES:NM.2">D_Lattice</a> &amp; <font color="Maroon" title="c2">L2</font> is   <a href="lattices.html#NM2" title="LATTICES:NM.2">D_Lattice</a> implies <span class="p1"><a href="filter_1.html#K7" title="FILTER_1:func.7">[:</a><span class="default"><font color="Maroon" title="c1">L1</font>,<font color="Maroon" title="c2">L2</font></span><a href="filter_1.html#K7" title="FILTER_1:func.7">:]</a></span> is   <a href="lattices.html#NM2" title="LATTICES:NM.2">D_Lattice</a> ) &amp; ( <span class="p1"><a href="filter_1.html#K7" title="FILTER_1:func.7">[:</a><span class="default"><font color="Maroon" title="c1">L1</font>,<font color="Maroon" title="c2">L2</font></span><a href="filter_1.html#K7" title="FILTER_1:func.7">:]</a></span> is   <a href="lattices.html#NM8" title="LATTICES:NM.8">B_Lattice</a> implies ( <span class="p1"><a href="filter_1.html#K7" title="FILTER_1:func.7">[:</a><span class="default"><font color="Maroon" title="c1">L1</font>,<font color="Maroon" title="c2">L2</font></span><a href="filter_1.html#K7" title="FILTER_1:func.7">:]</a></span> is   <a href="lattices.html#NM7" title="LATTICES:NM.7">C_Lattice</a> &amp; <span class="p1"><a href="filter_1.html#K7" title="FILTER_1:func.7">[:</a><span class="default"><font color="Maroon" title="c1">L1</font>,<font color="Maroon" title="c2">L2</font></span><a href="filter_1.html#K7" title="FILTER_1:func.7">:]</a></span> is   <a href="lattices.html#NM2" title="LATTICES:NM.2">D_Lattice</a> ) ) &amp; ( <span class="p1"><a href="filter_1.html#K7" title="FILTER_1:func.7">[:</a><span class="default"><font color="Maroon" title="c1">L1</font>,<font color="Maroon" title="c2">L2</font></span><a href="filter_1.html#K7" title="FILTER_1:func.7">:]</a></span> is   <a href="lattices.html#NM7" title="LATTICES:NM.7">C_Lattice</a> &amp; <span class="p1"><a href="filter_1.html#K7" title="FILTER_1:func.7">[:</a><span class="default"><font color="Maroon" title="c1">L1</font>,<font color="Maroon" title="c2">L2</font></span><a href="filter_1.html#K7" title="FILTER_1:func.7">:]</a></span> is   <a href="lattices.html#NM2" title="LATTICES:NM.2">D_Lattice</a> implies <span class="p1"><a href="filter_1.html#K7" title="FILTER_1:func.7">[:</a><span class="default"><font color="Maroon" title="c1">L1</font>,<font color="Maroon" title="c2">L2</font></span><a href="filter_1.html#K7" title="FILTER_1:func.7">:]</a></span> is   <a href="lattices.html#NM8" title="LATTICES:NM.8">B_Lattice</a> ) )
 
<b>by </b><i><a class="ref" href="filter_1.html#T39" target="_self" title="FILTER_1:th.39">Th39</a>, <a class="ref" href="filter_1.html#T46" target="_self" title="FILTER_1:th.46">Th46</a>, <a class="ref" href="lattices.html#D20" title="LATTICES:def.20">LATTICES:def 20</a></i>;<br/>
<b>hence </b><a NAME="E2:66"/>
( ( <font color="Maroon" title="c1">L1</font> is   <a href="lattices.html#NM8" title="LATTICES:NM.8">B_Lattice</a> &amp; <font color="Maroon" title="c2">L2</font> is   <a href="lattices.html#NM8" title="LATTICES:NM.8">B_Lattice</a> ) iff <span class="p1"><a href="filter_1.html#K7" title="FILTER_1:func.7">[:</a><span class="default"><font color="Maroon" title="c1">L1</font>,<font color="Maroon" title="c2">L2</font></span><a href="filter_1.html#K7" title="FILTER_1:func.7">:]</a></span> is   <a href="lattices.html#NM8" title="LATTICES:NM.8">B_Lattice</a> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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