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<b>let </b><font color="Maroon">L</font> be  <a href="yellow_0.html#V3">bounded</a> <a href="waybel_0.html#NM8">LATTICE</a>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:140"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">L</font> is <a href="waybel_1.html#V2" target="_self">distributive</a>
 <b>and </b><br/><a NAME="E2:140"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">L</font> is <a href="waybel_1.html#V10" target="_self">complemented</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>consider </b><font color="Maroon">x'</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font><b> such that </b><br/><a NAME="E4:140"/><i><font color="Green">E45</font></i>: 
<font color="Maroon">x'</font> <a href="waybel_1.html#R6" target="_self">is_a_complement_of</a> <font color="Maroon">x</font>
 <b>by </b><i>, <a class="ref" href="waybel_1.html#T10" target="_self">Th10</a></i>;<br/>
<b>take </b>
<font color="Maroon">x'</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/>

<span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x'</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font> = 
<span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x'</font></span>)</span>
<b>by </b><i>, </i>
<br/>.= 
<span class="p1">(<span class="default"><a href="yellow_0.html#K3">Bottom</a> <font color="Maroon">L</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span>
<b>by </b><i><a class="ref" href="waybel_1.html#T12" target="_self">Th12</a>, <a class="ref" href="waybel_1.html#D12" target="_self">Def12</a></i>
<br/>.= 
<font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font>
<b>by </b><i/>
;<br/>
<b>hence </b><a NAME="E6:140"/>
<span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x'</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">y</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T23">YELLOW_0:23</a></i>;<br/>

<span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x'</font> = 
<span class="p1">(<span class="default"><font color="Maroon">x'</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">x'</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span>
<b>by </b><i>, </i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">x'</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><a href="yellow_0.html#K4">Top</a> <font color="Maroon">L</font></span>)</span>
<b>by </b><i><a class="ref" href="waybel_1.html#T12" target="_self">Th12</a>, <a class="ref" href="waybel_1.html#D12" target="_self">Def12</a></i>
<br/>.= 
<font color="Maroon">x'</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font>
<b>by </b><i/>
;<br/>
<b>hence </b><a NAME="E8:140"/>
<font color="Maroon">y</font> <a href="orders_2.html#R3">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x'</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T22">YELLOW_0:22</a></i>;<br/>


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