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<span class="kw">set </span><font color="Maroon" title="c1">L</font> =  <a href="sheffer1.html#K4" title="SHEFFER1:func.4">TrivShefferOrthoLattStr</a> ;<br/>
<a NAME="E1:49_3_1"/><span class="lab"><font color="Green" title="E38">A1</font></span>: 
( ( 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 <a href="sheffer1.html#K4" title="SHEFFER1:func.4">TrivShefferOrthoLattStr</a>  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"><font color="Olive" title="b1">x</font> <a href="sheffer1.html#K5" title="SHEFFER1:func.5">|</a> <font color="Olive" title="b2">y</font></span>)</span> <a href="sheffer1.html#K5" title="SHEFFER1:func.5">|</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">x</font> <a href="sheffer1.html#K5" title="SHEFFER1:func.5">|</a> <font color="Olive" title="b2">y</font></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 <a href="sheffer1.html#K4" title="SHEFFER1:func.4">TrivShefferOrthoLattStr</a>  holds  <font color="Olive" title="b1">x</font> <a href="sheffer1.html#K5" title="SHEFFER1:func.5">|</a> <font color="Olive" title="b2">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.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="robbins1.html#K5" title="ROBBINS1: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> ) )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="struct_0.html#D10" title="STRUCT_0:def.10">STRUCT_0:def 10</a></span>;<br/>
<a NAME="E2:49_3_1"/>
( ( for <font color="Olive" title="b1">x</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="sheffer1.html#K4" title="SHEFFER1:func.4">TrivShefferOrthoLattStr</a>  holds  <font color="Olive" title="b1">x</font> <a href="sheffer1.html#K5" title="SHEFFER1:func.5">|</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> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a>  ) &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 <a href="sheffer1.html#K4" title="SHEFFER1:func.4">TrivShefferOrthoLattStr</a>  holds  <font color="Olive" title="b1">x</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Olive" title="b2">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">x</font> <a href="sheffer1.html#K5" title="SHEFFER1:func.5">|</a> <font color="Olive" title="b1">x</font></span>)</span> <a href="sheffer1.html#K5" title="SHEFFER1:func.5">|</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">y</font> <a href="sheffer1.html#K5" title="SHEFFER1:func.5">|</a> <font color="Olive" title="b2">y</font></span>)</span> ) )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="struct_0.html#D10" title="STRUCT_0:def.10">STRUCT_0:def 10</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:49_3_1"/>
 <a href="sheffer1.html#K4" title="SHEFFER1:func.4">TrivShefferOrthoLattStr</a>  is  <a href="sheffer1.html#V9" title="SHEFFER1:attr.9">properly_defined</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:49_3_1"><span class="lab"><font color="Green" title="E38">A1</font></span></a>, <a class="ref" href="sheffer1.html#D12" target="_self" title="SHEFFER1:def.12">Def12</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="sheffer1.html#K4" title="SHEFFER1:func.4">TrivShefferOrthoLattStr</a>  is  <a href="robbins1.html#V7" title="ROBBINS1:attr.7">well-complemented</a> </span><br/>

<a NAME="E4:49_3_1"/>
 <a href="sheffer1.html#K4" title="SHEFFER1:func.4">TrivShefferOrthoLattStr</a>  is  <a href="robbins1.html#V7" title="ROBBINS1:attr.7">well-complemented</a> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="49_3_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c2">a</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="sheffer1.html#K4" title="SHEFFER1:func.4">TrivShefferOrthoLattStr</a> ; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="robbins1.html#D10" title="ROBBINS1:def.10">ROBBINS1:def 10</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">a</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="Maroon" title="c2">a</font></span><br/>

<a NAME="E1:49_3_1_1"/>
( <font color="Maroon" title="c2">a</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattices.html#K6" title="LATTICES:func.6">Top</a> <a href="sheffer1.html#K4" title="SHEFFER1:func.4">TrivShefferOrthoLattStr</a>  &amp; <font color="Maroon" title="c2">a</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattices.html#K5" title="LATTICES:func.5">Bottom</a> <a href="sheffer1.html#K4" title="SHEFFER1:func.4">TrivShefferOrthoLattStr</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="struct_0.html#D10" title="STRUCT_0:def.10">STRUCT_0:def 10</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:49_3_1_1"/>
<font color="Maroon" title="c2">a</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="Maroon" title="c2">a</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="lattices.html#D18" title="LATTICES:def.18">LATTICES:def 18</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E5:49_3_1"/>
 <a href="sheffer1.html#K4" title="SHEFFER1:func.4">TrivShefferOrthoLattStr</a>  is  <a href="robbins1.html#V7" title="ROBBINS1:attr.7">well-complemented</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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