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<b>let </b><font color="Maroon">L</font> be  non <a href="struct_0.html#V3">empty</a> <a href="lattices.html#V10">Lattice-like</a> <a href="lattices.html#V17">Boolean</a> <a href="robbins1.html#V7">well-complemented</a> <a href="sheffer1.html#V9" target="_self">properly_defined</a>  <a href="sheffer1.html#L3" target="_self">ShefferOrthoLattStr</a> ;<br/><b>let </b><font color="Maroon">x</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>, <font color="Maroon">y</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>, <font color="Maroon">z</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="sheffer1.html#D15" target="_self">SHEFFER1:def 15</a><br/>



<a NAME="E1:52"/>
<font color="Maroon">x</font> <a href="robbins1.html#K6">*'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="robbins1.html#K3">`</a> </span>)</span> <a href="robbins1.html#K5">+</a> <span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="robbins1.html#K3">`</a> </span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="robbins1.html#K3">`</a> </span>)</span> <a href="robbins1.html#K6">*'</a> <font color="Maroon">x</font></span>)</span> <a href="robbins1.html#K5">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="robbins1.html#K3">`</a> </span>)</span> <a href="robbins1.html#K6">*'</a> <font color="Maroon">x</font></span>)</span>
 
<b>by </b><i><a class="ref" href="robbins1.html#T31">ROBBINS1:31</a></i>;<br/>
<a NAME="E2:52"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="robbins1.html#K3">`</a> </span>)</span> <a href="robbins1.html#K3">`</a> </span>)</span> <a href="robbins1.html#K6">*'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="robbins1.html#K3">`</a> </span>)</span> <a href="robbins1.html#K5">+</a> <span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="robbins1.html#K3">`</a> </span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="robbins1.html#K3">`</a> </span>)</span> <a href="robbins1.html#K6">*'</a> <font color="Maroon">x</font></span>)</span> <a href="robbins1.html#K5">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="robbins1.html#K3">`</a> </span>)</span> <a href="robbins1.html#K6">*'</a> <font color="Maroon">x</font></span>)</span>
 
<b>by </b><i><a class="ref" href="robbins1.html#T3">ROBBINS1:3</a></i>;<br/>
<a NAME="E3:52"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="robbins1.html#K3">`</a> </span>)</span> <a href="robbins1.html#K3">`</a> </span>)</span> <a href="robbins1.html#K6">*'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="robbins1.html#K3">`</a> </span>)</span> <a href="robbins1.html#K5">+</a> <span class="p4">(<span class="default"><font color="Maroon">z</font> <a href="robbins1.html#K3">`</a> </span>)</span></span>)</span> <a href="robbins1.html#K3">`</a> </span>)</span> <a href="robbins1.html#K3">`</a> </span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="robbins1.html#K3">`</a> </span>)</span> <a href="robbins1.html#K6">*'</a> <font color="Maroon">x</font></span>)</span> <a href="robbins1.html#K5">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="robbins1.html#K3">`</a> </span>)</span> <a href="robbins1.html#K6">*'</a> <font color="Maroon">x</font></span>)</span>
 
<b>by </b><i><a class="ref" href="robbins1.html#T3">ROBBINS1:3</a></i>;<br/>
<a NAME="E4:52"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="robbins1.html#K3">`</a> </span>)</span> <a href="robbins1.html#K5">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="robbins1.html#K3">`</a> </span>)</span> <a href="robbins1.html#K5">+</a> <span class="p4">(<span class="default"><font color="Maroon">z</font> <a href="robbins1.html#K3">`</a> </span>)</span></span>)</span> <a href="robbins1.html#K3">`</a> </span>)</span></span>)</span> <a href="robbins1.html#K3">`</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="robbins1.html#K3">`</a> </span>)</span> <a href="robbins1.html#K6">*'</a> <font color="Maroon">x</font></span>)</span> <a href="robbins1.html#K5">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="robbins1.html#K3">`</a> </span>)</span> <a href="robbins1.html#K6">*'</a> <font color="Maroon">x</font></span>)</span>
 
<b>by </b><i/>;<br/>
<a NAME="E5:52"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="robbins1.html#K3">`</a> </span>)</span> <a href="robbins1.html#K5">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">y</font> <a href="sheffer1.html#K5" target="_self">|</a> <font color="Maroon">z</font></span>)</span> <a href="robbins1.html#K3">`</a> </span>)</span></span>)</span> <a href="robbins1.html#K3">`</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="robbins1.html#K3">`</a> </span>)</span> <a href="robbins1.html#K6">*'</a> <font color="Maroon">x</font></span>)</span> <a href="robbins1.html#K5">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="robbins1.html#K3">`</a> </span>)</span> <a href="robbins1.html#K6">*'</a> <font color="Maroon">x</font></span>)</span>
 
<b>by </b><i><a class="ref" href="sheffer1.html#D8" target="_self">Def8</a></i>;<br/>
<a NAME="E6:52"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="sheffer1.html#K5" target="_self">|</a> <span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="sheffer1.html#K5" target="_self">|</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="robbins1.html#K3">`</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="robbins1.html#K3">`</a> </span>)</span> <a href="robbins1.html#K6">*'</a> <font color="Maroon">x</font></span>)</span> <a href="robbins1.html#K5">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="robbins1.html#K3">`</a> </span>)</span> <a href="robbins1.html#K6">*'</a> <font color="Maroon">x</font></span>)</span>
 
<b>by </b><i><a class="ref" href="sheffer1.html#D8" target="_self">Def8</a></i>;<br/>
<b>then </b><span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="sheffer1.html#K5" target="_self">|</a> <span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="sheffer1.html#K5" target="_self">|</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="sheffer1.html#K5" target="_self">|</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="sheffer1.html#K5" target="_self">|</a> <span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="sheffer1.html#K5" target="_self">|</a> <font color="Maroon">z</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="robbins1.html#K3">`</a> </span>)</span> <a href="robbins1.html#K6">*'</a> <font color="Maroon">x</font></span>)</span> <a href="robbins1.html#K5">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="robbins1.html#K3">`</a> </span>)</span> <a href="robbins1.html#K6">*'</a> <font color="Maroon">x</font></span>)</span>
<b>by </b><i><a class="ref" href="sheffer1.html#D8" target="_self">Def8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="robbins1.html#K3">`</a> </span>)</span> <a href="robbins1.html#K6">*'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="robbins1.html#K3">`</a> </span>)</span> <a href="robbins1.html#K3">`</a> </span>)</span></span>)</span> <a href="robbins1.html#K5">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="robbins1.html#K3">`</a> </span>)</span> <a href="robbins1.html#K6">*'</a> <font color="Maroon">x</font></span>)</span>
<b>by </b><i><a class="ref" href="robbins1.html#T3">ROBBINS1:3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="robbins1.html#K3">`</a> </span>)</span> <a href="robbins1.html#K6">*'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="robbins1.html#K3">`</a> </span>)</span> <a href="robbins1.html#K3">`</a> </span>)</span></span>)</span> <a href="robbins1.html#K5">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="robbins1.html#K3">`</a> </span>)</span> <a href="robbins1.html#K6">*'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="robbins1.html#K3">`</a> </span>)</span> <a href="robbins1.html#K3">`</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="robbins1.html#T3">ROBBINS1:3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="robbins1.html#K5">+</a> <span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="robbins1.html#K3">`</a> </span>)</span></span>)</span> <a href="robbins1.html#K3">`</a> </span>)</span> <a href="robbins1.html#K5">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="robbins1.html#K3">`</a> </span>)</span> <a href="robbins1.html#K6">*'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="robbins1.html#K3">`</a> </span>)</span> <a href="robbins1.html#K3">`</a> </span>)</span></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="robbins1.html#K5">+</a> <span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="robbins1.html#K3">`</a> </span>)</span></span>)</span> <a href="robbins1.html#K3">`</a> </span>)</span> <a href="robbins1.html#K5">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="robbins1.html#K5">+</a> <span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="robbins1.html#K3">`</a> </span>)</span></span>)</span> <a href="robbins1.html#K3">`</a> </span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="robbins1.html#K5">+</a> <span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="robbins1.html#K3">`</a> </span>)</span></span>)</span> <a href="sheffer1.html#K5" target="_self">|</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="robbins1.html#K5">+</a> <span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="robbins1.html#K3">`</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="sheffer1.html#D8" target="_self">Def8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">y</font> <a href="robbins1.html#K3">`</a> </span>)</span> <a href="robbins1.html#K3">`</a> </span>)</span> <a href="robbins1.html#K5">+</a> <span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="robbins1.html#K3">`</a> </span>)</span></span>)</span> <a href="sheffer1.html#K5" target="_self">|</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="robbins1.html#K5">+</a> <span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="robbins1.html#K3">`</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="robbins1.html#T3">ROBBINS1:3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">y</font> <a href="robbins1.html#K3">`</a> </span>)</span> <a href="robbins1.html#K3">`</a> </span>)</span> <a href="robbins1.html#K5">+</a> <span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="robbins1.html#K3">`</a> </span>)</span></span>)</span> <a href="sheffer1.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">z</font> <a href="robbins1.html#K3">`</a> </span>)</span> <a href="robbins1.html#K3">`</a> </span>)</span> <a href="robbins1.html#K5">+</a> <span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="robbins1.html#K3">`</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="robbins1.html#T3">ROBBINS1:3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="robbins1.html#K3">`</a> </span>)</span> <a href="sheffer1.html#K5" target="_self">|</a> <font color="Maroon">x</font></span>)</span> <a href="sheffer1.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">z</font> <a href="robbins1.html#K3">`</a> </span>)</span> <a href="robbins1.html#K3">`</a> </span>)</span> <a href="robbins1.html#K5">+</a> <span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="robbins1.html#K3">`</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="sheffer1.html#D8" target="_self">Def8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="robbins1.html#K3">`</a> </span>)</span> <a href="sheffer1.html#K5" target="_self">|</a> <font color="Maroon">x</font></span>)</span> <a href="sheffer1.html#K5" target="_self">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="robbins1.html#K3">`</a> </span>)</span> <a href="sheffer1.html#K5" target="_self">|</a> <font color="Maroon">x</font></span>)</span>
<b>by </b><i><a class="ref" href="sheffer1.html#D8" target="_self">Def8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="sheffer1.html#K5" target="_self">|</a> <font color="Maroon">y</font></span>)</span> <a href="sheffer1.html#K5" target="_self">|</a> <font color="Maroon">x</font></span>)</span> <a href="sheffer1.html#K5" target="_self">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="robbins1.html#K3">`</a> </span>)</span> <a href="sheffer1.html#K5" target="_self">|</a> <font color="Maroon">x</font></span>)</span>
<b>by </b><i><a class="ref" href="sheffer1.html#D8" target="_self">Def8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="sheffer1.html#K5" target="_self">|</a> <font color="Maroon">y</font></span>)</span> <a href="sheffer1.html#K5" target="_self">|</a> <font color="Maroon">x</font></span>)</span> <a href="sheffer1.html#K5" target="_self">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="sheffer1.html#K5" target="_self">|</a> <font color="Maroon">z</font></span>)</span> <a href="sheffer1.html#K5" target="_self">|</a> <font color="Maroon">x</font></span>)</span>
<b>by </b><i><a class="ref" href="sheffer1.html#D8" target="_self">Def8</a></i>
;<br/>
<b>hence </b><a NAME="E8:52"/>
<span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="sheffer1.html#K5" target="_self">|</a> <span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="sheffer1.html#K5" target="_self">|</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="sheffer1.html#K5" target="_self">|</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="sheffer1.html#K5" target="_self">|</a> <span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="sheffer1.html#K5" target="_self">|</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="sheffer1.html#K5" target="_self">|</a> <font color="Maroon">y</font></span>)</span> <a href="sheffer1.html#K5" target="_self">|</a> <font color="Maroon">x</font></span>)</span> <a href="sheffer1.html#K5" target="_self">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="sheffer1.html#K5" target="_self">|</a> <font color="Maroon">z</font></span>)</span> <a href="sheffer1.html#K5" target="_self">|</a> <font color="Maroon">x</font></span>)</span>
 ;<br/>


</div>
