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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  <a href="robbins1.html#V7" target="_self">well-complemented</a> <a href="robbins1.html#NM1">preOrthoLattice</a>;<br/>

<b>assume </b><a NAME="E1:112_2_1"/>
<font color="Maroon">c<sub>1</sub></font> is <a href="lattices.html#V17">Boolean</a>
 ;<br/>

<b>then reconsider </b><font color="Maroon">c<sub>2</sub></font> = <font color="Maroon">c<sub>1</sub></font> as  <a href="lattices.html#V17">Boolean</a> <a href="robbins1.html#V7" target="_self">well-complemented</a> <a href="robbins1.html#NM1">preOrthoLattice</a> ;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="112_2_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>2</sub></font>;<br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span></span>)</span> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span></span>)</span> <a href="robbins1.html#K3" target="_self">`</a>  = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="robbins1.html#T34" target="_self">Th34</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="lattices.html#K4">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="lattices.html#D11">LATTICES:def 11</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="lattices.html#K4">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="lattices.html#K4">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="lattices.html#D11">LATTICES:def 11</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="lattices.html#K4">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span></span>)</span> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="robbins1.html#T34" target="_self">Th34</a></i>
<br/>.= 
<font color="Maroon">c<sub>3</sub></font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="lattices.html#K4">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span></span>)</span> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="lattices.html#D9">LATTICES:def 9</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="lattices.html#K4">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span></span>)</span></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span></span>)</span> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span>
<b>by </b><i><a class="ref" href="lattices.html#D5">LATTICES:def 5</a></i>
<br/>.= 
<font color="Maroon">c<sub>3</sub></font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span></span>)</span> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span>
<b>by </b><i><a class="ref" href="lattices.html#D8">LATTICES:def 8</a></i>
<br/>.= 
<font color="Maroon">c<sub>3</sub></font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lattices.html#K6">Top</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span>
<b>by </b><i><a class="ref" href="robbins1.html#T61" target="_self">Th61</a></i>
<br/>.= 
<font color="Maroon">c<sub>3</sub></font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p1">(<span class="default"><a href="lattices.html#K5">Bottom</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="robbins1.html#T62" target="_self">Th62</a></i>
<br/>.= 
<font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="ref" href="lattices.html#T39">LATTICES:39</a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:112_2_1"/>
<font color="Maroon">c<sub>1</sub></font> is <a href="robbins1.html#V4" target="_self">Robbins</a>
 <b>by </b><i><a class="ref" href="robbins1.html#D5" target="_self">Def5</a></i>;<br/>


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