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

<b>let </b><font color="Maroon" title="c1">L</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a> <a href="lattices.html#V10" title="LATTICES:attr.10">Lattice-like</a> <a href="lattice3.html#V1" title="LATTICE3:attr.1">with_suprema</a> <a href="lattice3.html#V2" title="LATTICE3:attr.2">with_infima</a> <a href="oposet_1.html#V14" title="OPOSET_1:attr.14">PartialOrdered</a> <a href="oposet_1.html#V19" title="OPOSET_1:attr.19">OrderInvolutive</a> <a href="robbins3.html#V10" title="ROBBINS3:attr.10">naturally_sup-generated</a> <a href="robbins3.html#V11" title="ROBBINS3:attr.11">naturally_inf-generated</a>  <a href="robbins3.html#L4" title="ROBBINS3:struct.4">OrthoLattRelStr</a> ;<br/>

<a NAME="E1:92"/><i><font color="Green" title="E33">A1</font></i>: 
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  <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="robbins3.html#NK4" title="ROBBINS3:NK.4">"|_|"</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> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">x</font> <a href="robbins3.html#NK3" title="ROBBINS3:NK.3">"|^|"</a> <font color="Olive" title="b2">y</font></span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="92_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> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font>;<br/>

<b>set </b><font color="Maroon" title="c4">i</font> = <font color="Maroon" title="c2">a</font> <a href="robbins3.html#NK3" title="ROBBINS3:NK.3">"|^|"</a> <font color="Maroon" title="c3">b</font>;<br/>
<b>set </b><font color="Maroon" title="c5">s</font> = <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="robbins3.html#NK4" title="ROBBINS3:NK.4">"|_|"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span>;<br/>
<a NAME="E1:92_1"/>
( <font color="Maroon" title="c2">a</font> <a href="robbins3.html#NK3" title="ROBBINS3:NK.3">"|^|"</a> <font color="Maroon" title="c3">b</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c2">a</font> &amp; <font color="Maroon" title="c2">a</font> <a href="robbins3.html#NK3" title="ROBBINS3:NK.3">"|^|"</a> <font color="Maroon" title="c3">b</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c3">b</font> )
 
<b>by </b><i><a class="ref" href="yellow_0.html#T23" title="YELLOW_0:th.23">YELLOW_0:23</a></i>;<br/>
<a NAME="E2:92_1"/><b>then </b><i><font color="Green" title="E34">A2</font></i>: 
( <font color="Maroon" title="c2">a</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a>  <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="robbins3.html#NK3" title="ROBBINS3:NK.3">"|^|"</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a>  &amp; <font color="Maroon" title="c3">b</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a>  <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="robbins3.html#NK3" title="ROBBINS3:NK.3">"|^|"</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a>  )
 
<b>by </b><i><a class="ref" href="robbins3.html#T7" target="_self" title="ROBBINS3:th.7">Th7</a></i>;<br/>
<a NAME="E3:92_1"/><b>then </b><i><font color="Green" title="E35">A3</font></i>: 
<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="robbins3.html#NK4" title="ROBBINS3:NK.4">"|_|"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="robbins3.html#NK3" title="ROBBINS3:NK.3">"|^|"</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins3.html#NK4" title="ROBBINS3:NK.4">"|_|"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="waybel_1.html#T3" title="WAYBEL_1:th.3">WAYBEL_1:3</a></i>;<br/>
<a NAME="E4:92_1"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="robbins3.html#NK3" title="ROBBINS3:NK.3">"|^|"</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins3.html#NK4" title="ROBBINS3:NK.4">"|_|"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="robbins3.html#NK3" title="ROBBINS3:NK.3">"|^|"</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="robbins3.html#T24" target="_self" title="ROBBINS3:th.24">Th24</a>, <a class="txt" href="robbins3.html#E2:92_1"><i><font color="Green" title="E34">A2</font></i></a></i>;<br/>
<b>hence </b><a NAME="E5:92_1"/>
<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="robbins3.html#NK4" title="ROBBINS3:NK.4">"|_|"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="robbins3.html#NK3" title="ROBBINS3:NK.3">"|^|"</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> 
 <b>by </b><i><a class="ref" href="lattice3.html#T13" title="LATTICE3:th.13">LATTICE3:13</a>, <a class="txt" href="robbins3.html#E3:92_1"><i><font color="Green" title="E35">A3</font></i></a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E2:92"/><i><font color="Green" title="E34">A4</font></i>: 
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  <span class="p1">(<span class="default"><font color="Olive" title="b1">x</font> <a href="robbins3.html#NK4" title="ROBBINS3:NK.4">"|_|"</a> <font color="Olive" title="b2">y</font></span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a>  <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</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="robbins3.html#NK3" title="ROBBINS3:NK.3">"|^|"</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>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="92_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> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font>;<br/>

<b>set </b><font color="Maroon" title="c4">i</font> = <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="robbins3.html#NK3" title="ROBBINS3:NK.3">"|^|"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c5">s</font> = <font color="Maroon" title="c2">a</font> <a href="robbins3.html#NK4" title="ROBBINS3:NK.4">"|_|"</a> <font color="Maroon" title="c3">b</font>;<br/>
<a NAME="E1:92_2"/>
( <font color="Maroon" title="c2">a</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c2">a</font> <a href="robbins3.html#NK4" title="ROBBINS3:NK.4">"|_|"</a> <font color="Maroon" title="c3">b</font> &amp; <font color="Maroon" title="c3">b</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c2">a</font> <a href="robbins3.html#NK4" title="ROBBINS3:NK.4">"|_|"</a> <font color="Maroon" title="c3">b</font> )
 
<b>by </b><i><a class="ref" href="yellow_0.html#T22" title="YELLOW_0:th.22">YELLOW_0:22</a></i>;<br/>
<a NAME="E2:92_2"/><b>then </b><i><font color="Green" title="E35">A5</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="robbins3.html#NK4" title="ROBBINS3:NK.4">"|_|"</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a>  <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c2">a</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a>  &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="robbins3.html#NK4" title="ROBBINS3:NK.4">"|_|"</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a>  <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c3">b</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a>  )
 
<b>by </b><i><a class="ref" href="robbins3.html#T7" target="_self" title="ROBBINS3:th.7">Th7</a></i>;<br/>
<a NAME="E3:92_2"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="robbins3.html#NK4" title="ROBBINS3:NK.4">"|_|"</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins3.html#NK3" title="ROBBINS3:NK.3">"|^|"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</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="robbins3.html#NK3" title="ROBBINS3:NK.3">"|^|"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="waybel_1.html#T2" title="WAYBEL_1:th.2">WAYBEL_1:2</a></i>;<br/>
<b>hence </b><a NAME="E4:92_2"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="robbins3.html#NK4" title="ROBBINS3:NK.4">"|_|"</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a>  <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</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="robbins3.html#NK3" title="ROBBINS3:NK.3">"|^|"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span>
 <b>by </b><i><a class="ref" href="robbins3.html#T24" target="_self" title="ROBBINS3:th.24">Th24</a>, <a class="txt" href="robbins3.html#E2:92_2"><i><font color="Green" title="E35">A5</font></i></a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E3:92"/>
<font color="Maroon" title="c1">L</font> is <a href="robbins1.html#V9" title="ROBBINS1:attr.9">de_Morgan</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="92_3"><b>proof </b></a><div class="add">

<a NAME="E1:92_3"/>
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  <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">x</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins3.html#K5" title="ROBBINS3:func.5">|_|</a> <span class="p2">(<span class="default"><font color="Olive" title="b2">y</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span></span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">x</font> <a href="robbins3.html#K4" title="ROBBINS3:func.4">|^|</a> <font color="Olive" title="b2">y</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="92_3_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> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font>;<br/>

<b>set </b><font color="Maroon" title="c4">s</font> = <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="robbins3.html#NK4" title="ROBBINS3:NK.4">"|_|"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c5">i</font> = <font color="Maroon" title="c2">a</font> <a href="robbins3.html#NK3" title="ROBBINS3:NK.3">"|^|"</a> <font color="Maroon" title="c3">b</font>;<br/>
<a NAME="E1:92_3_1"/><i><font color="Green" title="E35">A6</font></i>: 
<font color="Maroon" title="c2">a</font> <a href="robbins3.html#NK3" title="ROBBINS3:NK.3">"|^|"</a> <font color="Maroon" title="c3">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">a</font> <a href="robbins3.html#K4" title="ROBBINS3:func.4">|^|</a> <font color="Maroon" title="c3">b</font>
 
<b>by </b><i><a class="ref" href="robbins3.html#T26" target="_self" title="ROBBINS3:th.26">Th26</a></i>;<br/>
<a NAME="E2:92_3_1"/><i><font color="Green" title="E36">A7</font></i>: 
<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="robbins3.html#NK4" title="ROBBINS3:NK.4">"|_|"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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="robbins3.html#K5" title="ROBBINS3:func.5">|_|</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="robbins3.html#T25" target="_self" title="ROBBINS3:th.25">Th25</a></i>;<br/>
<a NAME="E3:92_3_1"/>
( <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="robbins1.html#K3" title="ROBBINS1:func.3">`</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">a</font> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">b</font> )
 
<b>by </b><i><a class="ref" href="robbins3.html#T6" target="_self" title="ROBBINS3:th.6">Th6</a></i>;<br/>
<a NAME="E4:92_3_1"/><b>then </b><i><font color="Green" title="E37">A8</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins3.html#NK4" title="ROBBINS3:NK.4">"|_|"</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span></span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a>  <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c2">a</font> <a href="robbins3.html#NK3" title="ROBBINS3:NK.3">"|^|"</a> <font color="Maroon" title="c3">b</font>
 
<b>by </b><i><a class="txt" href="robbins3.html#E2:92"><i><font color="Green" title="E34">A4</font></i></a></i>;<br/>
<a NAME="E5:92_3_1"/>
<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="robbins3.html#NK4" title="ROBBINS3:NK.4">"|_|"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="robbins3.html#NK3" title="ROBBINS3:NK.3">"|^|"</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> 
 
<b>by </b><i><a class="txt" href="robbins3.html#E1:92"><i><font color="Green" title="E33">A1</font></i></a></i>;<br/>
<a NAME="E6:92_3_1"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="robbins3.html#NK3" title="ROBBINS3:NK.3">"|^|"</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a>  <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins3.html#NK4" title="ROBBINS3:NK.4">"|_|"</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span></span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> 
 
<b>by </b><i><a class="ref" href="robbins3.html#T7" target="_self" title="ROBBINS3:th.7">Th7</a></i>;<br/>
<a NAME="E7:92_3_1"/><b>then </b>
<font color="Maroon" title="c2">a</font> <a href="robbins3.html#NK3" title="ROBBINS3:NK.3">"|^|"</a> <font color="Maroon" title="c3">b</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins3.html#NK4" title="ROBBINS3:NK.4">"|_|"</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span></span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> 
 
<b>by </b><i><a class="ref" href="robbins3.html#T6" target="_self" title="ROBBINS3:th.6">Th6</a></i>;<br/>
<b>hence </b><a NAME="E8:92_3_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins3.html#K5" title="ROBBINS3:func.5">|_|</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span></span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">a</font> <a href="robbins3.html#K4" title="ROBBINS3:func.4">|^|</a> <font color="Maroon" title="c3">b</font>
 <b>by </b><i><a class="txt" href="robbins3.html#E1:92_3_1"><i><font color="Green" title="E35">A6</font></i></a>, <a class="txt" href="robbins3.html#E2:92_3_1"><i><font color="Green" title="E36">A7</font></i></a>, <a class="txt" href="robbins3.html#E4:92_3_1"><i><font color="Green" title="E37">A8</font></i></a>, <a class="ref" href="orders_2.html#T25" title="ORDERS_2:th.25">ORDERS_2:25</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E2:92_3"/>
<font color="Maroon" title="c1">L</font> is <a href="robbins1.html#V9" title="ROBBINS1:attr.9">de_Morgan</a>
 <b>by </b><i><a class="ref" href="robbins1.html#D23" title="ROBBINS1:def.23">ROBBINS1:def 23</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E4:92"/>
<font color="Maroon" title="c1">L</font> is <a href="robbins1.html#V9" title="ROBBINS1:attr.9">de_Morgan</a>
 ;<br/>


</div>
