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

<span class="kw">let </span><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#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#V13" title="OPOSET_1:attr.13">PartialOrdered</a>   <a href="oposet_1.html#V18" title="OPOSET_1:attr.18">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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">L</font> is  <a href="robbins1.html#V9" title="ROBBINS1:attr.9">de_Morgan</a> </span><br/>

<a NAME="E1:92"/><span class="lab"><font color="Green" title="E33">A1</font></span>: 
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"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <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> </span><br/>

<span class="kw">set </span><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/>
<span class="kw">set </span><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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#T23" title="YELLOW_0:th.23">YELLOW_0:23</a></span>;<br/>
<a NAME="E2:92_1"/><span class="kw">then </span>
<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> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="robbins3.html#T7" target="_self" title="ROBBINS3:th.7">Th7</a></span>;<br/>
<a NAME="E3:92_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E34">A2</font></span>: 
<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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="waybel_1.html#T3" title="WAYBEL_1:th.3">WAYBEL_1:3</a></span>;<br/>
<a NAME="E4:92_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="c3">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#T23" title="YELLOW_0:th.23">YELLOW_0:23</a></span>;<br/>
<a NAME="E5:92_1"/><span class="kw">then </span>
<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> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="robbins3.html#T7" target="_self" title="ROBBINS3:th.7">Th7</a></span>;<br/>
<a NAME="E6:92_1"/><span class="kw">then </span>
<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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="robbins3.html#T24" target="_self" title="ROBBINS3:th.24">Th24</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:92_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> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:92_1"><span class="lab"><font color="Green" title="E34">A2</font></span></a>, <a class="ref" href="lattice3.html#T13" title="LATTICE3:th.13">LATTICE3:13</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E2:92"/><span class="lab"><font color="Green" title="E34">A3</font></span>: 
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"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <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></span><br/>

<span class="kw">set </span><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/>
<span class="kw">set </span><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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#T22" title="YELLOW_0:th.22">YELLOW_0:22</a></span>;<br/>
<a NAME="E2:92_2"/><span class="kw">then </span>
<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> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="robbins3.html#T7" target="_self" title="ROBBINS3:th.7">Th7</a></span>;<br/>
<a NAME="E3:92_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E35">A4</font></span>: 
<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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="waybel_1.html#T2" title="WAYBEL_1:th.2">WAYBEL_1:2</a></span>;<br/>
<a NAME="E4:92_2"/>
<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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#T22" title="YELLOW_0:th.22">YELLOW_0:22</a></span>;<br/>
<a NAME="E5:92_2"/><span class="kw">then </span>
<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> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="robbins3.html#T7" target="_self" title="ROBBINS3:th.7">Th7</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:92_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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:92_2"><span class="lab"><font color="Green" title="E35">A4</font></span></a>, <a class="ref" href="robbins3.html#T24" target="_self" title="ROBBINS3:th.24">Th24</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E3:92"/>
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"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <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></span><br/>

<span class="kw">set </span><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/>
<span class="kw">set </span><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"/>
( <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> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="robbins3.html#T6" target="_self" title="ROBBINS3:th.6">Th6</a></span>;<br/>
<a NAME="E2:92_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E35">A5</font></span>: 
<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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:92"><span class="lab"><font color="Green" title="E34">A3</font></span></a></span>;<br/>
<a NAME="E3:92_3"/>
<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> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:92"><span class="lab"><font color="Green" title="E33">A1</font></span></a>, <a class="ref" href="robbins3.html#T7" target="_self" title="ROBBINS3:th.7">Th7</a></span>;<br/>
<a NAME="E4:92_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E36">A6</font></span>: 
<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> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="robbins3.html#T6" target="_self" title="ROBBINS3:th.6">Th6</a></span>;<br/>
<a NAME="E5:92_3"/>
( <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> &amp; <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> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="robbins3.html#T25" target="_self" title="ROBBINS3:th.25">Th25</a>, <a class="ref" href="robbins3.html#T26" target="_self" title="ROBBINS3:th.26">Th26</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:92_3"/>
<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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:92_3"><span class="lab"><font color="Green" title="E35">A5</font></span></a>, <a class="txt" href="#E4:92_3"><span class="lab"><font color="Green" title="E36">A6</font></span></a>, <a class="ref" href="orders_2.html#T25" title="ORDERS_2:th.25">ORDERS_2:25</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E4:92"/>
<font color="Maroon" title="c1">L</font> is  <a href="robbins1.html#V9" title="ROBBINS1:attr.9">de_Morgan</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="robbins1.html#D23" title="ROBBINS1:def.23">ROBBINS1:def 23</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
