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

<b>assume </b><a NAME="E1:35"/><i><font color="Green">E17</font></i>: 
the <a href="lattices.html#U2">L_join</a> of <font color="Maroon">L</font> <a href="binop_1.html#R6">is_distributive_wrt</a> the <a href="lattices.html#U1">L_meet</a> of <font color="Maroon">L</font>
 ;<br/>

<a NAME="E2:35"/><i><font color="Green">E18</font></i>: 
for <font color="Olive">a</font>, <font color="Olive">b</font>, <font color="Olive">c</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> holds  <font color="Olive">a</font> <a href="lattices.html#K3">"\/"</a> <span class="p1">(<span class="default"><font color="Olive">b</font> <a href="lattices.html#K4">"/\"</a> <font color="Olive">c</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Olive">a</font> <a href="lattices.html#K3">"\/"</a> <font color="Olive">b</font></span>)</span> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><font color="Olive">a</font> <a href="lattices.html#K3">"\/"</a> <font color="Olive">c</font></span>)</span>
 
<b>by </b><i><a class="ref" href="lattice2.html#T9" target="_self">Th9</a>, <a class="ref" href="binop_1.html#T24">BINOP_1:24</a></i>;<br/>
<b>let </b><font color="Maroon">a</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="lattices.html#D11">LATTICES:def 11</a><br/><b>let </b><font color="Maroon">b</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>;<br/><b>let </b><font color="Maroon">c</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>;<br/>





<b>thus </b><font color="Maroon">a</font> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">c</font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="lattices.html#K4">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">c</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">c</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">b</font></span>)</span>
<b>by </b><i><a class="ref" href="lattices.html#D9">LATTICES:def 9</a></i>
<br/>.= 
<font color="Maroon">a</font> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">a</font></span>)</span> <a href="lattices.html#K4">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">c</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">b</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="lattices.html#D7">LATTICES:def 7</a></i>
<br/>.= 
<font color="Maroon">a</font> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">b</font></span>)</span> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">c</font></span>)</span>
<b>by </b><i><a class="ref" href="lattice2.html#T10" target="_self">Th10</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">b</font></span>)</span> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">a</font></span>)</span> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">b</font></span>)</span> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">c</font></span>)</span>
<b>by </b><i><a class="ref" href="lattices.html#D8">LATTICES:def 8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">b</font></span>)</span> <a href="lattices.html#K3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">c</font></span>)</span>
<b>by </b><i><a class="ref" href="lattice2.html#T10" target="_self">Th10</a></i>
;<br/>


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