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<b>let </b><font color="Maroon">L</font> be  <a href="lattices.html#V11">distributive</a> <a href="robbins1.html#V7" target="_self">well-complemented</a> <a href="robbins1.html#NM1">preOrthoLattice</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/>



<a NAME="E1:60"/><i><font color="Green">E27</font></i>: 
<font color="Maroon">x</font> <a href="robbins1.html#K3" target="_self">`</a>  <a href="lattices.html#R2">is_a_complement_of</a> <font color="Maroon">x</font>
 
<b>by </b><i/>;<br/>
<a NAME="E2:60"/>
<span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span> <a href="robbins1.html#K3" target="_self">`</a>  <a href="lattices.html#R2">is_a_complement_of</a> <font color="Maroon">x</font> <a href="robbins1.html#K3" target="_self">`</a> 
 
<b>by </b><i/>;<br/>
<a NAME="E3:60"/><b>then </b><i><font color="Green">E35</font></i>: 
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span> <a href="hidden.html#R1">=</a>  <a href="lattices.html#K6">Top</a> <font color="Maroon">L</font> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span> <a href="hidden.html#R1">=</a>  <a href="lattices.html#K5">Bottom</a> <font color="Maroon">L</font> )
 
<b>by </b><i><a class="ref" href="lattices.html#D18">LATTICES:def 18</a></i>;<br/>
<a NAME="E4:60"/>
( <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="lattices.html#K6">Top</a> <font color="Maroon">L</font> &amp; <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="lattices.html#K5">Bottom</a> <font color="Maroon">L</font> )
 
<b>by </b><i>, <a class="ref" href="lattices.html#D18">LATTICES:def 18</a></i>;<br/>
<b>hence </b><a NAME="E5:60"/>
<span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span> <a href="robbins1.html#K3" target="_self">`</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">x</font>
 <b>by </b><i><a class="ref" href="robbins1.html#T7" target="_self">Th7</a>, <a class="ref" href="lattices.html#T32">LATTICES:32</a></i>;<br/>


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