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

<b>let </b><font color="Maroon" title="c1">L</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="lattices.html#L3" title="LATTICES:struct.3">LattStr</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">L</font> is <a href="lattices.html#V10" title="LATTICES:attr.10">Lattice-like</a> iff ( <font color="Maroon" title="c1">L</font> is <a href="robbins3.html#V2" title="ROBBINS3:attr.2">meet-Associative</a> &amp; <font color="Maroon" title="c1">L</font> is <a href="robbins3.html#V1" title="ROBBINS3:attr.1">join-Associative</a> &amp; <font color="Maroon" title="c1">L</font> is <a href="robbins3.html#V3" title="ROBBINS3:attr.3">meet-Absorbing</a> &amp; <font color="Maroon" title="c1">L</font> is <a href="lattices.html#V9" title="LATTICES:attr.9">join-absorbing</a> ) )</span><br/>

<a NAME="E1:8"/><i><font color="Green" title="E9">A1</font></i>: 
( <font color="Maroon" title="c1">L</font> is <a href="lattices.html#V10" title="LATTICES:attr.10">Lattice-like</a> implies ( <font color="Maroon" title="c1">L</font> is <a href="robbins3.html#V2" title="ROBBINS3:attr.2">meet-Associative</a> &amp; <font color="Maroon" title="c1">L</font> is <a href="robbins3.html#V1" title="ROBBINS3:attr.1">join-Associative</a> &amp; <font color="Maroon" title="c1">L</font> is <a href="robbins3.html#V3" title="ROBBINS3:attr.3">meet-Absorbing</a> &amp; <font color="Maroon" title="c1">L</font> is <a href="lattices.html#V9" title="LATTICES:attr.9">join-absorbing</a> ) )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="8_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:8_1"/><i><font color="Green" title="E10">A2</font></i>: 
<font color="Maroon" title="c1">L</font> is <a href="lattices.html#V10" title="LATTICES:attr.10">Lattice-like</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">L</font> is <a href="robbins3.html#V2" title="ROBBINS3:attr.2">meet-Associative</a> &amp; <font color="Maroon" title="c1">L</font> is <a href="robbins3.html#V1" title="ROBBINS3:attr.1">join-Associative</a> &amp; <font color="Maroon" title="c1">L</font> is <a href="robbins3.html#V3" title="ROBBINS3:attr.3">meet-Absorbing</a> &amp; <font color="Maroon" title="c1">L</font> is <a href="lattices.html#V9" title="LATTICES:attr.9">join-absorbing</a> )</span><br/>

<a NAME="E2:8_1"/><b>then </b><i><font color="Green" title="E11">A3</font></i>: 
( <font color="Maroon" title="c1">L</font> is <a href="lattices.html#V8" title="LATTICES:attr.8">meet-absorbing</a> &amp; <font color="Maroon" title="c1">L</font> is <a href="lattices.html#V9" title="LATTICES:attr.9">join-absorbing</a> )
 
<b>by </b><i><a class="ref" href="lattices.html#D10" title="LATTICES:def.10">LATTICES:def 10</a></i>;<br/>
<a NAME="E3:8_1"/><i><font color="Green" title="E12">A4</font></i>: 
( <font color="Maroon" title="c1">L</font> is <a href="lattices.html#V7" title="LATTICES:attr.7">meet-associative</a> &amp; <font color="Maroon" title="c1">L</font> is <a href="lattices.html#V6" title="LATTICES:attr.6">meet-commutative</a> &amp; <font color="Maroon" title="c1">L</font> is <a href="lattices.html#V5" title="LATTICES:attr.5">join-associative</a> &amp; <font color="Maroon" title="c1">L</font> is <a href="lattices.html#V4" title="LATTICES:attr.4">join-commutative</a> )
 
<b>by </b><i><a class="txt" href="robbins3.html#E1:8_1"><i><font color="Green" title="E10">A2</font></i></a>, <a class="ref" href="lattices.html#D10" title="LATTICES:def.10">LATTICES:def 10</a></i>;<br/>
<a NAME="E4:8_1"/><i><font color="Green" title="E13">A5</font></i>: 
for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font>, <font color="Olive" title="b3">z</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font> holds  <font color="Olive" title="b1">x</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">y</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Olive" title="b3">z</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">y</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">x</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Olive" title="b3">z</font></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="8_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">b</font>, <font color="Maroon" title="c4">c</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">a</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c4">c</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">b</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c4">c</font></span>)</span></span><br/>

<font color="Maroon" title="c2">a</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c4">c</font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c4">c</font>
<b>by </b><i><a class="txt" href="robbins3.html#E3:8_1"><i><font color="Green" title="E12">A4</font></i></a>, <a class="ref" href="lattices.html#D5" title="LATTICES:def.5">LATTICES:def 5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c2">a</font></span>)</span> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c4">c</font>
<b>by </b><i><a class="txt" href="robbins3.html#E3:8_1"><i><font color="Green" title="E12">A4</font></i></a>, <a class="ref" href="lattices.html#D4" title="LATTICES:def.4">LATTICES:def 4</a></i>
<br/>.= 
<font color="Maroon" title="c3">b</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c4">c</font></span>)</span>
<b>by </b><i><a class="txt" href="robbins3.html#E3:8_1"><i><font color="Green" title="E12">A4</font></i></a>, <a class="ref" href="lattices.html#D5" title="LATTICES:def.5">LATTICES:def 5</a></i>
;<br/>
<b>hence </b><a NAME="E2:8_1_1"/>
<font color="Maroon" title="c2">a</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c4">c</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">b</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c4">c</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E5:8_1"/><i><font color="Green" title="E14">A6</font></i>: 
for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font>, <font color="Olive" title="b3">z</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font> holds  <font color="Olive" title="b1">x</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">y</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Olive" title="b3">z</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">y</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">x</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Olive" title="b3">z</font></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="8_1_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">b</font>, <font color="Maroon" title="c4">c</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">a</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c4">c</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">b</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c4">c</font></span>)</span></span><br/>

<font color="Maroon" title="c2">a</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c4">c</font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c4">c</font>
<b>by </b><i><a class="txt" href="robbins3.html#E3:8_1"><i><font color="Green" title="E12">A4</font></i></a>, <a class="ref" href="lattices.html#D7" title="LATTICES:def.7">LATTICES:def 7</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c2">a</font></span>)</span> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c4">c</font>
<b>by </b><i><a class="txt" href="robbins3.html#E3:8_1"><i><font color="Green" title="E12">A4</font></i></a>, <a class="ref" href="lattices.html#D6" title="LATTICES:def.6">LATTICES:def 6</a></i>
<br/>.= 
<font color="Maroon" title="c3">b</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c4">c</font></span>)</span>
<b>by </b><i><a class="txt" href="robbins3.html#E3:8_1"><i><font color="Green" title="E12">A4</font></i></a>, <a class="ref" href="lattices.html#D7" title="LATTICES:def.7">LATTICES:def 7</a></i>
;<br/>
<b>hence </b><a NAME="E2:8_1_2"/>
<font color="Maroon" title="c2">a</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c4">c</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">b</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c4">c</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E6:8_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="c1">L</font> holds  <font color="Olive" title="b1">x</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">x</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Olive" title="b2">y</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">x</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="8_1_3"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">b</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">a</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">a</font></span><br/>

<font color="Maroon" title="c2">a</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c2">a</font></span>)</span> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c2">a</font>
<b>by </b><i><a class="txt" href="robbins3.html#E2:8_1"><i><font color="Green" title="E11">A3</font></i></a>, <a class="ref" href="lattices.html#D8" title="LATTICES:def.8">LATTICES:def 8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c2">a</font>
<b>by </b><i><a class="txt" href="robbins3.html#E3:8_1"><i><font color="Green" title="E12">A4</font></i></a>, <a class="ref" href="lattices.html#D6" title="LATTICES:def.6">LATTICES:def 6</a></i>
<br/>.= 
<font color="Maroon" title="c2">a</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c3">b</font></span>)</span>
<b>by </b><i><a class="txt" href="robbins3.html#E3:8_1"><i><font color="Green" title="E12">A4</font></i></a>, <a class="ref" href="lattices.html#D4" title="LATTICES:def.4">LATTICES:def 4</a></i>
;<br/>
<b>hence </b><a NAME="E2:8_1_3"/>
<font color="Maroon" title="c2">a</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">a</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E7:8_1"/>
( <font color="Maroon" title="c1">L</font> is <a href="robbins3.html#V2" title="ROBBINS3:attr.2">meet-Associative</a> &amp; <font color="Maroon" title="c1">L</font> is <a href="robbins3.html#V1" title="ROBBINS3:attr.1">join-Associative</a> &amp; <font color="Maroon" title="c1">L</font> is <a href="robbins3.html#V3" title="ROBBINS3:attr.3">meet-Absorbing</a> &amp; <font color="Maroon" title="c1">L</font> is <a href="lattices.html#V9" title="LATTICES:attr.9">join-absorbing</a> )
 <b>by </b><i><a class="txt" href="robbins3.html#E1:8_1"><i><font color="Green" title="E10">A2</font></i></a>, <a class="txt" href="robbins3.html#E4:8_1"><i><font color="Green" title="E13">A5</font></i></a>, <a class="txt" href="robbins3.html#E5:8_1"><i><font color="Green" title="E14">A6</font></i></a>, <a class="ref" href="robbins3.html#D1" target="_self" title="ROBBINS3:def.1">Def1</a>, <a class="ref" href="robbins3.html#D2" target="_self" title="ROBBINS3:def.2">Def2</a>, <a class="ref" href="robbins3.html#D3" target="_self" title="ROBBINS3:def.3">Def3</a>, <a class="ref" href="lattices.html#D10" title="LATTICES:def.10">LATTICES:def 10</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E2:8"/>
( <font color="Maroon" title="c1">L</font> is <a href="robbins3.html#V2" title="ROBBINS3:attr.2">meet-Associative</a> &amp; <font color="Maroon" title="c1">L</font> is <a href="robbins3.html#V1" title="ROBBINS3:attr.1">join-Associative</a> &amp; <font color="Maroon" title="c1">L</font> is <a href="robbins3.html#V3" title="ROBBINS3:attr.3">meet-Absorbing</a> &amp; <font color="Maroon" title="c1">L</font> is <a href="lattices.html#V9" title="LATTICES:attr.9">join-absorbing</a> implies <font color="Maroon" title="c1">L</font> is <a href="lattices.html#V10" title="LATTICES:attr.10">Lattice-like</a> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="8_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:8_2"/><i><font color="Green" title="E10">A7</font></i>: 
( <font color="Maroon" title="c1">L</font> is <a href="robbins3.html#V2" title="ROBBINS3:attr.2">meet-Associative</a> &amp; <font color="Maroon" title="c1">L</font> is <a href="robbins3.html#V1" title="ROBBINS3:attr.1">join-Associative</a> &amp; <font color="Maroon" title="c1">L</font> is <a href="robbins3.html#V3" title="ROBBINS3:attr.3">meet-Absorbing</a> &amp; <font color="Maroon" title="c1">L</font> is <a href="lattices.html#V9" title="LATTICES:attr.9">join-absorbing</a> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">L</font> is <a href="lattices.html#V10" title="LATTICES:attr.10">Lattice-like</a></span><br/>

<a NAME="E2:8_2"/><b>then </b><i><font color="Green" title="E11">A8</font></i>: 
( <font color="Maroon" title="c1">L</font> is <a href="lattices.html#V6" title="LATTICES:attr.6">meet-commutative</a> &amp; <font color="Maroon" title="c1">L</font> is <a href="lattices.html#V4" title="LATTICES:attr.4">join-commutative</a> )
 
<b>by </b><i><a class="ref" href="robbins3.html#T2" target="_self" title="ROBBINS3:th.2">Th2</a></i>;<br/>
<a NAME="E3:8_2"/><i><font color="Green" title="E12">A9</font></i>: 
( <font color="Maroon" title="c1">L</font> is <a href="lattices.html#V7" title="LATTICES:attr.7">meet-associative</a> &amp; <font color="Maroon" title="c1">L</font> is <a href="lattices.html#V5" title="LATTICES:attr.5">join-associative</a> )
 
<b>by </b><i><a class="txt" href="robbins3.html#E1:8_2"><i><font color="Green" title="E10">A7</font></i></a>, <a class="ref" href="robbins3.html#T4" target="_self" title="ROBBINS3:th.4">Th4</a></i>;<br/>
<a NAME="E4:8_2"/>
<font color="Maroon" title="c1">L</font> is <a href="lattices.html#V8" title="LATTICES:attr.8">meet-absorbing</a>
 
<b>by </b><i><a class="txt" href="robbins3.html#E1:8_2"><i><font color="Green" title="E10">A7</font></i></a>, <a class="ref" href="robbins3.html#T3" target="_self" title="ROBBINS3:th.3">Th3</a></i>;<br/>
<b>hence </b><a NAME="E5:8_2"/>
<font color="Maroon" title="c1">L</font> is <a href="lattices.html#V10" title="LATTICES:attr.10">Lattice-like</a>
 <b>by </b><i><a class="txt" href="robbins3.html#E1:8_2"><i><font color="Green" title="E10">A7</font></i></a>, <a class="txt" href="robbins3.html#E2:8_2"><i><font color="Green" title="E11">A8</font></i></a>, <a class="txt" href="robbins3.html#E3:8_2"><i><font color="Green" title="E12">A9</font></i></a>, <a class="ref" href="lattices.html#D10" title="LATTICES:def.10">LATTICES:def 10</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:8"/>
( <font color="Maroon" title="c1">L</font> is <a href="lattices.html#V10" title="LATTICES:attr.10">Lattice-like</a> iff ( <font color="Maroon" title="c1">L</font> is <a href="robbins3.html#V2" title="ROBBINS3:attr.2">meet-Associative</a> &amp; <font color="Maroon" title="c1">L</font> is <a href="robbins3.html#V1" title="ROBBINS3:attr.1">join-Associative</a> &amp; <font color="Maroon" title="c1">L</font> is <a href="robbins3.html#V3" title="ROBBINS3:attr.3">meet-Absorbing</a> &amp; <font color="Maroon" title="c1">L</font> is <a href="lattices.html#V9" title="LATTICES:attr.9">join-absorbing</a> ) )
 <b>by </b><i><a class="txt" href="robbins3.html#E1:8"><i><font color="Green" title="E9">A1</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
