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<a NAME="E1:47_1_1"/>
( the <a href="lattices.html#U2" title="LATTICES:sel.2">L_join</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">L</font> <a href="lattice2.html#K1" title="LATTICE2:func.1">.:</a> </span>)</span> is <a href="binop_1.html#V1" title="BINOP_1:attr.1">commutative</a> &amp; the <a href="lattices.html#U2" title="LATTICES:sel.2">L_join</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">L</font> <a href="lattice2.html#K1" title="LATTICE2:func.1">.:</a> </span>)</span> is <a href="binop_1.html#V2" title="BINOP_1:attr.2">associative</a> &amp; the <a href="lattices.html#U1" title="LATTICES:sel.1">L_meet</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">L</font> <a href="lattice2.html#K1" title="LATTICE2:func.1">.:</a> </span>)</span> is <a href="binop_1.html#V1" title="BINOP_1:attr.1">commutative</a> &amp; the <a href="lattices.html#U1" title="LATTICES:sel.1">L_meet</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">L</font> <a href="lattice2.html#K1" title="LATTICE2:func.1">.:</a> </span>)</span> is <a href="binop_1.html#V2" title="BINOP_1:attr.2">associative</a> &amp; the <a href="lattices.html#U2" title="LATTICES:sel.2">L_join</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">L</font> <a href="lattice2.html#K1" title="LATTICE2:func.1">.:</a> </span>)</span> <a href="lattice2.html#R1" title="LATTICE2:pred.1">absorbs</a> the <a href="lattices.html#U1" title="LATTICES:sel.1">L_meet</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">L</font> <a href="lattice2.html#K1" title="LATTICE2:func.1">.:</a> </span>)</span> &amp; the <a href="lattices.html#U1" title="LATTICES:sel.1">L_meet</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">L</font> <a href="lattice2.html#K1" title="LATTICE2:func.1">.:</a> </span>)</span> <a href="lattice2.html#R1" title="LATTICE2:pred.1">absorbs</a> the <a href="lattices.html#U2" title="LATTICES:sel.2">L_join</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">L</font> <a href="lattice2.html#K1" title="LATTICE2:func.1">.:</a> </span>)</span> )
 
<b>by </b><i><a class="ref" href="lattice2.html#T40" target="_self" title="LATTICE2:th.40">Th40</a>, <a class="ref" href="lattice2.html#T41" target="_self" title="LATTICE2:th.41">Th41</a></i>;<br/>
<b>hence </b><a NAME="E2:47_1_1"/>
<font color="Maroon" title="c1">L</font> <a href="lattice2.html#K1" title="LATTICE2:func.1">.:</a>  is <a href="lattices.html#V10" title="LATTICES:attr.10">Lattice-like</a>
 <b>by </b><i><a class="ref" href="lattice2.html#T17" target="_self" title="LATTICE2:th.17">Th17</a></i>; <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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