<?xml version="1.0"?>
<div class="add">

<b>take </b>
 <a href="sheffer1.html#K4">TrivShefferOrthoLattStr</a> 
;<br/>

<a NAME="E1:73_1_1"/>
 <a href="sheffer1.html#K4">TrivShefferOrthoLattStr</a>  is <a href="robbins1.html#V9">de_Morgan</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="73_1_1_1"><b>proof </b></a><div class="add">

<a NAME="E1:73_1_1_1"/>
for <font color="Olive">x</font>, <font color="Olive">y</font> being  <a href="struct_0.html#NM1">Element</a> of <a href="sheffer1.html#K4">TrivShefferOrthoLattStr</a>  holds  <font color="Olive">x</font> <a href="lattices.html#K4">"/\"</a> <font color="Olive">y</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive">x</font> <a href="robbins1.html#K3">`</a> </span>)</span> <a href="lattices.html#K3">"\/"</a> <span class="p2">(<span class="default"><font color="Olive">y</font> <a href="robbins1.html#K3">`</a> </span>)</span></span>)</span> <a href="robbins1.html#K3">`</a> 
 
<b>by </b><i><a class="ref" href="realset2.html#D7">REALSET2:def 7</a></i>;<br/>
<b>hence </b><a NAME="E2:73_1_1_1"/>
 <a href="sheffer1.html#K4">TrivShefferOrthoLattStr</a>  is <a href="robbins1.html#V9">de_Morgan</a>
 <b>by </b><i><a class="ref" href="robbins1.html#D23">ROBBINS1:def 23</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E2:73_1_1"/>
(  <a href="sheffer1.html#K4">TrivShefferOrthoLattStr</a>  is <a href="sheffer1.html#V9">properly_defined</a> &amp;  <a href="sheffer1.html#K4">TrivShefferOrthoLattStr</a>  is <a href="lattices.html#V17">Boolean</a> &amp;  <a href="sheffer1.html#K4">TrivShefferOrthoLattStr</a>  is <a href="robbins1.html#V7">well-complemented</a> &amp;  <a href="sheffer1.html#K4">TrivShefferOrthoLattStr</a>  is <a href="lattices.html#V10">Lattice-like</a> &amp;  <a href="sheffer1.html#K4">TrivShefferOrthoLattStr</a>  is <a href="robbins1.html#V9">de_Morgan</a> &amp;  <a href="sheffer1.html#K4">TrivShefferOrthoLattStr</a>  is <a href="sheffer1.html#V10">satisfying_Sheffer_1</a> &amp;  <a href="sheffer1.html#K4">TrivShefferOrthoLattStr</a>  is <a href="sheffer1.html#V11">satisfying_Sheffer_2</a> &amp;  <a href="sheffer1.html#K4">TrivShefferOrthoLattStr</a>  is <a href="sheffer1.html#V12">satisfying_Sheffer_3</a> &amp;  <a href="sheffer1.html#K4">TrivShefferOrthoLattStr</a>  is <a href="sheffer2.html#V1" target="_self">satisfying_Sh_1</a> )
 ;<br/>


</div>
