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

<b>let </b><font color="Maroon">L</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="lattices.html#L3">LattStr</a> ;<br/>

<b>assume </b><a NAME="E1:4"/><i><font color="Green">E22</font></i>: 
( <font color="Maroon">L</font> is <a href="robbins3.html#V2" target="_self">meet-Associative</a> &amp; <font color="Maroon">L</font> is <a href="robbins3.html#V1" target="_self">join-Associative</a> &amp; <font color="Maroon">L</font> is <a href="robbins3.html#V3" target="_self">meet-Absorbing</a> &amp; <font color="Maroon">L</font> is <a href="lattices.html#V9">join-absorbing</a> )
 ;<br/>

<a NAME="E2:4"/><i><font color="Green">E23</font></i>: 
for <font color="Olive">x</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> holds  <font color="Olive">x</font> <a href="lattices.html#K2">"/\"</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a> <font color="Olive">x</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="4_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">a</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>;<br/>

<a NAME="E1:4_1"/>
<font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="lattices.html#K2">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="lattices.html#K1">"\/"</a> <font color="Maroon">a</font></span>)</span>
 
<b>by </b><i><a class="ref" href="lattices.html#D9">LATTICES:def 9</a>, </i>;<br/>
<b>hence </b><a NAME="E2:4_1"/>
<font color="Maroon">a</font> <a href="lattices.html#K2">"/\"</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font>
 <b>by </b><i>, </i>;<br/>


</div><b>end;</b></div>
<a NAME="E3:4"/>
for <font color="Olive">x</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> holds  <font color="Olive">x</font> <a href="lattices.html#K1">"\/"</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a> <font color="Olive">x</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="4_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">a</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>;<br/>

<a NAME="E1:4_2"/>
<font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="lattices.html#K1">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="lattices.html#K2">"/\"</a> <font color="Maroon">a</font></span>)</span>
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E2:4_2"/>
<font color="Maroon">a</font> <a href="lattices.html#K1">"\/"</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font>
 <b>by </b><i><a class="ref" href="lattices.html#D9">LATTICES:def 9</a>, </i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E4:4"/>
( <font color="Maroon">L</font> is <a href="sheffer1.html#V5">meet-idempotent</a> &amp; <font color="Maroon">L</font> is <a href="robbins1.html#V6">join-idempotent</a> )
 <b>by </b><i>, <a class="ref" href="sheffer1.html#D9">SHEFFER1:def 9</a>, <a class="ref" href="robbins1.html#D7">ROBBINS1:def 7</a></i>;<br/>


</div>
