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<span class="kw">let </span><font color="Maroon" title="c1">L</font> be   <a href="robbins1.html#V8" title="ROBBINS1:attr.8">well-complemented</a>  <a href="robbins1.html#NM1" title="ROBBINS1:NM.1">preOrthoLattice</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">L</font> is  <a href="lattices.html#V17" title="LATTICES:attr.17">Boolean</a>  implies <font color="Maroon" title="c1">L</font> is  <a href="robbins1.html#V6" title="ROBBINS1:attr.6">Huntington</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:110_1_1"/><span class="lab"><font color="Green" title="E61">A1</font></span>: 
<font color="Maroon" title="c1">L</font> is  <a href="lattices.html#V17" title="LATTICES:attr.17">Boolean</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">L</font> is  <a href="robbins1.html#V6" title="ROBBINS1:attr.6">Huntington</a> </span><br/>

<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c2">L9</font> = <font color="Maroon" title="c1">L</font> as   <a href="lattices.html#V17" title="LATTICES:attr.17">Boolean</a>  <a href="robbins1.html#NM1" title="ROBBINS1:NM.1">preOrthoLattice</a> ;<br/>
<a NAME="E3:110_1_1"/><span class="lab"><font color="Green" title="E62">A2</font></span>: 
 for <font color="Olive" title="b1">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">L9</font> holds  <span class="p1">(<span class="default"><a href="lattices.html#K6" title="LATTICES:func.6">Top</a> <font color="Maroon" title="c2">L9</font></span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">x</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="lattices.html#T17" title="LATTICES:th.17">LATTICES:17</a></span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="110_1_1_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c3">x</font>, <font color="Maroon" title="c4">y</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a></span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">y</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a></span>)</span></span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a></span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a></span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c4">y</font></span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">x</font></span><br/><span class="kw">thus </span><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a></span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">y</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a></span>)</span></span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a></span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a></span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c4">y</font></span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c4">y</font></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <font color="Maroon" title="c4">y</font></span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:110_1_1"><span class="lab"><font color="Green" title="E61">A1</font></span></a>, <a class="ref" href="robbins1.html#T33" target="_self" title="ROBBINS1:th.33">Th34</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <font color="Maroon" title="c4">y</font></span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a></span>)</span></span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">y</font> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <font color="Maroon" title="c4">y</font></span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:110_1_1"><span class="lab"><font color="Green" title="E61">A1</font></span></a>, <a class="ref" href="lattices.html#T11" title="LATTICES:th.11">LATTICES:11</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c4">y</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a></span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a></span>)</span></span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a></span>)</span></span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">y</font> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <font color="Maroon" title="c4">y</font></span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:110_1_1"><span class="lab"><font color="Green" title="E61">A1</font></span></a>, <a class="ref" href="robbins1.html#T32" target="_self" title="ROBBINS1:th.32">Th33</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">y</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a></span>)</span></span>)</span></span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">y</font> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <font color="Maroon" title="c4">y</font></span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:110_1_1"><span class="lab"><font color="Green" title="E61">A1</font></span></a>, <a class="ref" href="robbins1.html#T33" target="_self" title="ROBBINS1:th.33">Th34</a></span>
<br/>.= 
<font color="Maroon" title="c3">x</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">y</font> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <font color="Maroon" title="c4">y</font></span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="lattices.html#D8" title="LATTICES:def.8">LATTICES:def 8</a></span>
<br/>.= 
<font color="Maroon" title="c3">x</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">y</font> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c4">y</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a></span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a></span>)</span></span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:110_1_1"><span class="lab"><font color="Green" title="E61">A1</font></span></a>, <a class="ref" href="robbins1.html#T32" target="_self" title="ROBBINS1:th.32">Th33</a></span>
<br/>.= 
<font color="Maroon" title="c3">x</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">y</font> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">y</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:110_1_1"><span class="lab"><font color="Green" title="E61">A1</font></span></a>, <a class="ref" href="robbins1.html#T33" target="_self" title="ROBBINS1:th.33">Th34</a></span>
<br/>.= 
<font color="Maroon" title="c3">x</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">y</font> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <font color="Maroon" title="c3">x</font></span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">y</font> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">y</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:110_1_1"><span class="lab"><font color="Green" title="E61">A1</font></span></a>, <a class="ref" href="lattices.html#T11" title="LATTICES:th.11">LATTICES:11</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">y</font> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <font color="Maroon" title="c3">x</font></span>)</span></span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">y</font> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">y</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="lattices.html#D7" title="LATTICES:def.7">LATTICES:def 7</a></span>
<br/>.= 
<font color="Maroon" title="c3">x</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">y</font> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">y</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="lattices.html#D9" title="LATTICES:def.9">LATTICES:def 9</a></span>
<br/>.= 
<font color="Maroon" title="c3">x</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p1">(<span class="default"><a href="lattices.html#K6" title="LATTICES:func.6">Top</a> <font color="Maroon" title="c1">L</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="robbins1.html#T59" target="_self" title="ROBBINS1:th.59">Th61</a></span>
<br/>.= 
<font color="Maroon" title="c3">x</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:110_1_1"><span class="lab"><font color="Green" title="E62">A2</font></span></a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E5:110_1_1"/>
<font color="Maroon" title="c1">L</font> is  <a href="robbins1.html#V6" title="ROBBINS1:attr.6">Huntington</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="robbins1.html#D6" target="_self" title="ROBBINS1:def.6">Def6</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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