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<b>let </b><font color="Maroon">L</font> be   <a href="lattices.html#NM1">Lattice</a>;<br/><b>let </b><font color="Maroon">X</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>;<br/><b>let </b><font color="Maroon">Y</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>;<br/><b>let </b><font color="Maroon">Z</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>;<br/>







<b>thus </b><a NAME="E1:10"/>
( <font color="Maroon">X</font> <a href="boolealg.html#R1" target="_self">=</a> <font color="Maroon">Y</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">Z</font> implies ( <font color="Maroon">Y</font> <a href="lattices.html#R3">[=</a> <font color="Maroon">X</font> &amp; <font color="Maroon">Z</font> <a href="lattices.html#R3">[=</a> <font color="Maroon">X</font> &amp; ( for <font color="Olive">V</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>  st <font color="Maroon">Y</font> <a href="lattices.html#R3">[=</a> <font color="Olive">V</font> &amp; <font color="Maroon">Z</font> <a href="lattices.html#R3">[=</a> <font color="Olive">V</font> holds <br/><font color="Maroon">X</font> <a href="lattices.html#R3">[=</a> <font color="Olive">V</font> ) ) )
 <b>by </b><i>, <a class="ref" href="lattices.html#T22">LATTICES:22</a></i>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E2:10"/><i><font color="Green">E12</font></i>: 
<font color="Maroon">Y</font> <a href="lattices.html#R3">[=</a> <font color="Maroon">X</font>
 <b>and </b><br/><a NAME="E3:10"/><i><font color="Green">E13</font></i>: 
<font color="Maroon">Z</font> <a href="lattices.html#R3">[=</a> <font color="Maroon">X</font>
 <b>and </b><br/><a NAME="E4:10"/><i><font color="Green">E14</font></i>: 
for <font color="Olive">V</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>  st <font color="Maroon">Y</font> <a href="lattices.html#R3">[=</a> <font color="Olive">V</font> &amp; <font color="Maroon">Z</font> <a href="lattices.html#R3">[=</a> <font color="Olive">V</font> holds <br/><font color="Maroon">X</font> <a href="lattices.html#R3">[=</a> <font color="Olive">V</font>
 ;<br/>

<a NAME="E5:10"/>
( <font color="Maroon">Y</font> <a href="lattices.html#R3">[=</a> <font color="Maroon">Y</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">Z</font> &amp; <font color="Maroon">Z</font> <a href="lattices.html#R3">[=</a> <font color="Maroon">Y</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">Z</font> )
 
<b>by </b><i><a class="ref" href="lattices.html#T22">LATTICES:22</a></i>;<br/>
<a NAME="E6:10"/><b>then </b><i><font color="Green">E15</font></i>: 
<font color="Maroon">X</font> <a href="lattices.html#R3">[=</a> <font color="Maroon">Y</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">Z</font>
 
<b>by </b><i/>;<br/>
<a NAME="E7:10"/>
<font color="Maroon">Y</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">Z</font> <a href="lattices.html#R3">[=</a> <font color="Maroon">X</font>
 
<b>by </b><i>, , </i>;<br/>
<b>hence </b><a NAME="E8:10"/>
<font color="Maroon">X</font> <a href="boolealg.html#R1" target="_self">=</a> <font color="Maroon">Y</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">Z</font>
 <b>by </b><i>, <a class="ref" href="lattices.html#T26">LATTICES:26</a></i>;<br/>


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