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<span class="kw">let </span><font color="Maroon" title="c1">L</font> be  1 <a href="struct_0.html#V13" title="STRUCT_0:attr.13">-element</a>   <a href="robbins1.html#L4" title="ROBBINS1:struct.4">OrthoLattStr</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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="robbins3.html#V8" title="ROBBINS3:attr.8">involutive</a>  &amp; <font color="Maroon" title="c1">L</font> is  <a href="robbins3.html#V9" title="ROBBINS3:attr.9">with_Top</a>  &amp; <font color="Maroon" title="c1">L</font> is  <a href="robbins1.html#V10" title="ROBBINS1:attr.10">de_Morgan</a>  &amp; <font color="Maroon" title="c1">L</font> is  <a href="robbins1.html#V8" title="ROBBINS1:attr.8">well-complemented</a>  )</span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c2">L9</font> = <font color="Maroon" title="c1">L</font> as  1 <a href="struct_0.html#V13" title="STRUCT_0:attr.13">-element</a>   <a href="robbins1.html#L4" title="ROBBINS1:struct.4">OrthoLattStr</a>  ;<br/>
<a NAME="E2:64_1_1"/><span class="lab"><font color="Green" title="E23">A1</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"><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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="struct_0.html#D10" onmouseover="rs('struct_0/D10')" onmouseout="rh()">STRUCT_0:def 10</a></span>;<br/>
<a NAME="E3:64_1_1"/><span class="lab"><font color="Green" title="E24">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  <font color="Olive" title="b1">x</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a>  <a href="lattices.html#R2" title="LATTICES:pred.2">is_a_complement_of</a> <font color="Olive" title="b1">x</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="struct_0.html#D10" onmouseover="rs('struct_0/D10')" onmouseout="rh()">STRUCT_0:def 10</a></span>;<br/>
<a NAME="E4:64_1_1"/>
( (  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">L9</font> holds  <font color="Olive" title="b1">x</font> <a href="robbins3.html#NK1" title="ROBBINS3:NK.1">|_|</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#NK1" title="ROBBINS3:NK.1">|_|</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> ) &amp; (  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">L9</font> holds  <font color="Olive" title="b1">x</font> <a href="robbins3.html#NK2" title="ROBBINS3:NK.2">|^|</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="robbins3.html#NK1" title="ROBBINS3:NK.1">|_|</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>  ) )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="struct_0.html#D10" onmouseover="rs('struct_0/D10')" onmouseout="rh()">STRUCT_0:def 10</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:64_1_1"/>
( <font color="Maroon" title="c1">L</font> is  <a href="robbins3.html#V8" title="ROBBINS3:attr.8">involutive</a>  &amp; <font color="Maroon" title="c1">L</font> is  <a href="robbins3.html#V9" title="ROBBINS3:attr.9">with_Top</a>  &amp; <font color="Maroon" title="c1">L</font> is  <a href="robbins1.html#V10" title="ROBBINS1:attr.10">de_Morgan</a>  &amp; <font color="Maroon" title="c1">L</font> is  <a href="robbins1.html#V8" title="ROBBINS1:attr.8">well-complemented</a>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:64_1_1"><span class="lab"><font color="Green" title="E23">A1</font></span></a>, <a class="txt" href="#E3:64_1_1"><span class="lab"><font color="Green" title="E24">A2</font></span></a>, <a class="ref" href="robbins1.html#D10" onmouseover="rs('robbins1/D10')" onmouseout="rh()">ROBBINS1:def 10</a>, <a class="ref" href="robbins1.html#D23" onmouseover="rs('robbins1/D23')" onmouseout="rh()">ROBBINS1:def 23</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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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