<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon" title="c1">L</font> be   <a href="lattices.html#NM1" title="LATTICES:NM.1">Lattice</a>;<br/>

<b>thus </b><a NAME="E1:63"/>
( <font color="Maroon" title="c1">L</font> is   <a href="lattices.html#NM2" title="LATTICES:NM.2">D_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#NM2" title="LATTICES:NM.2">D_Lattice</a> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="63_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:63_1"/>
<font color="Maroon" title="c1">L</font> is   <a href="lattices.html#NM2" title="LATTICES:NM.2">D_Lattice</a>
 ;<br/>

<a NAME="E2:63_1"/><b>then </b>
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="binop_1.html#R6" title="BINOP_1:pred.6">is_distributive_wrt</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>
 
<b>by </b><i><a class="ref" href="lattice2.html#T37" target="_self" title="LATTICE2:th.37">Th37</a></i>;<br/>
<b>hence </b><a NAME="E3:63_1"/>
<font color="Maroon" title="c1">L</font> <a href="lattice2.html#K1" title="LATTICE2:func.1">.:</a>  is   <a href="lattices.html#NM2" title="LATTICES:NM.2">D_Lattice</a>
 <b>by </b><i><a class="ref" href="lattice2.html#T36" target="_self" title="LATTICE2:th.36">Th36</a></i>;<br/>


</div><b>end;</b></div>

<b>assume </b><a NAME="E2:63"/>
<font color="Maroon" title="c1">L</font> <a href="lattice2.html#K1" title="LATTICE2:func.1">.:</a>  is   <a href="lattices.html#NM2" title="LATTICES:NM.2">D_Lattice</a>
 ;<br/>

<a NAME="E3:63"/><b>then </b>
the <a href="lattices.html#U2" title="LATTICES:sel.2">L_join</a> of <font color="Maroon" title="c1">L</font> <a href="binop_1.html#R6" title="BINOP_1:pred.6">is_distributive_wrt</a> the <a href="lattices.html#U1" title="LATTICES:sel.1">L_meet</a> of <font color="Maroon" title="c1">L</font>
 
<b>by </b><i><a class="ref" href="lattice2.html#T37" target="_self" title="LATTICE2:th.37">Th37</a></i>;<br/>
<b>hence </b><a NAME="E4:63"/>
<font color="Maroon" title="c1">L</font> is   <a href="lattices.html#NM2" title="LATTICES:NM.2">D_Lattice</a>
 <b>by </b><i><a class="ref" href="lattice2.html#T36" target="_self" title="LATTICE2:th.36">Th36</a></i>;<br/>


</div>
