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<b>let </b><font color="Maroon" title="c1">L</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="robbins1.html#L3" title="ROBBINS1:struct.3">OrthoLattStr</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">L</font> is <a href="lattices.html#V17" title="LATTICES:attr.17">Boolean</a> &amp; <font color="Maroon" title="c1">L</font> is <a href="robbins1.html#V7" title="ROBBINS1:attr.7">well-complemented</a> &amp; <font color="Maroon" title="c1">L</font> is <a href="lattices.html#V10" title="LATTICES:attr.10">Lattice-like</a> implies <font color="Maroon" title="c1">L</font> is   <a href="robbins3.html#NM1" title="ROBBINS3:NM.1">Ortholattice</a> )</span><br/>

<b>assume </b><a NAME="E1:97"/>
( <font color="Maroon" title="c1">L</font> is <a href="lattices.html#V17" title="LATTICES:attr.17">Boolean</a> &amp; <font color="Maroon" title="c1">L</font> is <a href="robbins1.html#V7" title="ROBBINS1:attr.7">well-complemented</a> &amp; <font color="Maroon" title="c1">L</font> is <a href="lattices.html#V10" title="LATTICES:attr.10">Lattice-like</a> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">L</font> is   <a href="robbins3.html#NM1" title="ROBBINS3:NM.1">Ortholattice</a></span><br/>

<b>then reconsider </b><font color="Maroon" title="c2">L'</font> = <font color="Maroon" title="c1">L</font> as  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="lattices.html#V10" title="LATTICES:attr.10">Lattice-like</a> <a href="lattices.html#V17" title="LATTICES:attr.17">Boolean</a> <a href="robbins1.html#V7" title="ROBBINS1:attr.7">well-complemented</a>  <a href="robbins1.html#L3" title="ROBBINS1:struct.3">OrthoLattStr</a>  ;<br/>
<a NAME="E3:97"/><i><font color="Green" title="E35">A1</font></i>: 
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">L'</font> holds  <span class="p1">(<span class="default"><font color="Olive" title="b1">x</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">x</font>
 
<b>by </b><i><a class="ref" href="robbins1.html#T3" title="ROBBINS1:th.3">ROBBINS1:3</a></i>;<br/>
<a NAME="E4:97"/><i><font color="Green" title="E36">A2</font></i>: 
for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">L'</font> holds  <font color="Olive" title="b1">x</font> <a href="robbins3.html#K5" title="ROBBINS3:func.5">|_|</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">x</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">y</font> <a href="robbins3.html#K5" title="ROBBINS3:func.5">|_|</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">y</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="robbins1.html#T4" title="ROBBINS1:th.4">ROBBINS1:4</a></i>;<br/>
<a NAME="E5:97"/>
for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">L'</font> holds  <font color="Olive" title="b1">x</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Olive" title="b2">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">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="p2">(<span class="default"><font color="Olive" title="b2">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> 
 
<b>by </b><i><a class="ref" href="robbins1.html#T34" title="ROBBINS1:th.34">ROBBINS1:34</a></i>;<br/>
<b>hence </b><a NAME="E6:97"/>
<font color="Maroon" title="c1">L</font> is   <a href="robbins3.html#NM1" title="ROBBINS3:NM.1">Ortholattice</a>
 <b>by </b><i><a class="txt" href="robbins3.html#E3:97"><i><font color="Green" title="E35">A1</font></i></a>, <a class="txt" href="robbins3.html#E4:97"><i><font color="Green" title="E36">A2</font></i></a>, <a class="ref" href="robbins3.html#D6" target="_self" title="ROBBINS3:def.6">Def6</a>, <a class="ref" href="robbins3.html#D7" target="_self" title="ROBBINS3:def.7">Def7</a>, <a class="ref" href="robbins1.html#D23" title="ROBBINS1:def.23">ROBBINS1:def 23</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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