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

<b>let </b><font color="Maroon">G</font> be  non <a href="struct_0.html#V3">empty</a> <a href="lattices.html#V4">join-commutative</a> <a href="lattices.html#V5">join-associative</a> <a href="robbins1.html#V4" target="_self">Robbins</a>  <a href="robbins1.html#L2" target="_self">ComplLattStr</a> ;<br/>

<b>given </b><font color="Maroon">C</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">G</font>, <font color="Maroon">D</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">G</font><b> such that </b><a NAME="E1:99"/><i><font color="Green">E27</font></i>: 
<font color="Maroon">C</font> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">D</font> <a href="hidden.html#R1">=</a> <font color="Maroon">C</font>
 ;<br/>

<a NAME="E2:99"/><i><font color="Green">E35</font></i>: 
 <a href="robbins1.html#NK11" target="_self">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <font color="Maroon">C</font></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <span class="p2">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p3">(<span class="default"><font color="Maroon">D</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p4">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <font color="Maroon">C</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">D</font>
 
<b>by </b><i>, </i>;<br/>
<div><i><font color="Green">E36</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="99_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">G</font>;<br/><b>let </b><font color="Maroon">y</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">G</font>;<br/><b>thus </b> <a href="robbins1.html#NK11" target="_self">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">D</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p5">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p0">(<span class="default"><font color="Maroon">C</font> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <span class="p2">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">C</font> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">x</font></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">y</font></span>)</span></span>)</span></span>)</span> = 
 <a href="robbins1.html#NK11" target="_self">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p5">(<span class="default"><font color="Maroon">C</font> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <span class="p4">(<span class="default"><font color="Maroon">D</font> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">y</font></span>)</span></span>)</span></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <span class="p2">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">C</font> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">D</font></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">x</font></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">y</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="lattices.html#D5">LATTICES:def 5</a></i>
<br/>.= 
 <a href="robbins1.html#NK11" target="_self">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p5">(<span class="default"><font color="Maroon">C</font> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <span class="p4">(<span class="default"><font color="Maroon">D</font> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">y</font></span>)</span></span>)</span></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <span class="p2">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">C</font> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">x</font></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">D</font></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">y</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="lattices.html#D5">LATTICES:def 5</a></i>
<br/>.= 
 <a href="robbins1.html#NK11" target="_self">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p5">(<span class="default"><font color="Maroon">C</font> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <span class="p4">(<span class="default"><font color="Maroon">D</font> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">y</font></span>)</span></span>)</span></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <span class="p2">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">C</font> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">x</font></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <span class="p4">(<span class="default"><font color="Maroon">D</font> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">y</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="lattices.html#D5">LATTICES:def 5</a></i>
<br/>.= 
<font color="Maroon">D</font> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">y</font>
<b>by </b><i/>
;<br/></div><b>end;</b></div>
<div><i><font color="Green">E47</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="99_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">G</font>;<br/><b>let </b><font color="Maroon">y</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">G</font>;<br/><b>let </b><font color="Maroon">z</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">G</font>;<br/><b>set </b><font color="Maroon">k</font> = <span class="p1">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <font color="Maroon">x</font></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <span class="p1">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">y</font></span>)</span></span>)</span>;<br/><b>thus </b> <a href="robbins1.html#NK11" target="_self">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <font color="Maroon">x</font></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <span class="p5">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p0">(<span class="default"><font color="Maroon">x</font> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">y</font></span>)</span></span>)</span></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <span class="p2">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p3">(<span class="default"><font color="Maroon">y</font> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">z</font></span>)</span></span>)</span></span>)</span> = 
 <a href="robbins1.html#NK11" target="_self">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <font color="Maroon">x</font></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <span class="p5">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p0">(<span class="default"><font color="Maroon">x</font> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">y</font></span>)</span></span>)</span></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <span class="p2">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <font color="Maroon">x</font></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <span class="p0">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">y</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">z</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i/>
<br/>.= 
<font color="Maroon">z</font>
<b>by </b><i/>
;<br/></div><b>end;</b></div>
<div><i><font color="Green">E73</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="99_3"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">G</font>;<br/><b>let </b><font color="Maroon">y</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">G</font>;<br/><b>let </b><font color="Maroon">z</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">G</font>;<br/><b>set </b><font color="Maroon">k</font> =  <a href="robbins1.html#NK11" target="_self">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <font color="Maroon">x</font></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">y</font></span>)</span>;<br/><b>thus </b> <a href="robbins1.html#NK11" target="_self">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <font color="Maroon">x</font></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">x</font></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">y</font></span>)</span> = 
 <a href="robbins1.html#NK11" target="_self">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <font color="Maroon">x</font></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">x</font></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <span class="p2">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <font color="Maroon">x</font></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <span class="p4">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p5">(<span class="default"><font color="Maroon">x</font> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">y</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i/>
<br/>.= 
 <a href="robbins1.html#NK11" target="_self">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <font color="Maroon">x</font></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">y</font></span>)</span></span>)</span></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <span class="p2">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <font color="Maroon">x</font></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <span class="p4">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p5">(<span class="default"><font color="Maroon">x</font> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">y</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="lattices.html#D5">LATTICES:def 5</a></i>
<br/>.= 
 <a href="robbins1.html#NK11" target="_self">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <font color="Maroon">x</font></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">y</font></span>)</span>
<b>by </b><i/>
;<br/></div><b>end;</b></div>
<div><i><font color="Green">E74</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="99_4"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">G</font>;<br/><b>thus </b><font color="Maroon">D</font> = 
 <a href="robbins1.html#NK11" target="_self">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <font color="Maroon">x</font></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">C</font></span>)</span></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <span class="p5">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p0">(<span class="default"><font color="Maroon">x</font> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">C</font></span>)</span></span>)</span></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">D</font></span>)</span></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <span class="p2">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p3">(<span class="default"><font color="Maroon">C</font> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">D</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i/>
<br/>.= 
 <a href="robbins1.html#NK11" target="_self">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <font color="Maroon">C</font></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <span class="p2">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">D</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p5">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p0">(<span class="default"><font color="Maroon">C</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p1">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <span class="p4">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p5">(<span class="default"><font color="Maroon">C</font> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="lattices.html#D5">LATTICES:def 5</a></i>
;<br/></div><b>end;</b></div>
<b>set </b><font color="Maroon">E</font> = <font color="Maroon">D</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p1">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <font color="Maroon">C</font></span>)</span>;<br/>
<b>set </b><font color="Maroon">L</font> =  <a href="robbins1.html#NK11" target="_self">-</a> <span class="p1">(<span class="default"><font color="Maroon">D</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p2">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <font color="Maroon">C</font></span>)</span></span>)</span>;<br/>
<a NAME="E7:99"/><i><font color="Green">E75</font></i>: 
 <a href="robbins1.html#NK11" target="_self">-</a> <span class="p1">(<span class="default"><font color="Maroon">D</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p2">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p3">(<span class="default"><font color="Maroon">C</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p4">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p5">(<span class="default"><font color="Maroon">D</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p0">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <font color="Maroon">C</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="robbins1.html#NK11" target="_self">-</a> <span class="p1">(<span class="default"><font color="Maroon">D</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p2">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <font color="Maroon">C</font></span>)</span></span>)</span>
 
<b>by </b><i>, </i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="99_5"><b>now </b></a><div class="add"><b>thus </b> <a href="robbins1.html#NK11" target="_self">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p3">(<span class="default"><font color="Maroon">D</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p4">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <font color="Maroon">C</font></span>)</span></span>)</span></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <span class="p2">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p3">(<span class="default"><font color="Maroon">C</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p4">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p5">(<span class="default"><font color="Maroon">D</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p0">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <font color="Maroon">C</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> = 
 <a href="robbins1.html#NK11" target="_self">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p3">(<span class="default"><font color="Maroon">D</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p4">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p5">(<span class="default"><font color="Maroon">C</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p0">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p1">(<span class="default"><font color="Maroon">D</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p2">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <font color="Maroon">C</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <span class="p2">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">D</font> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">C</font></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <span class="p4">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p5">(<span class="default"><font color="Maroon">D</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p0">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <font color="Maroon">C</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i>, , </i>
<br/>.= 
 <a href="robbins1.html#NK11" target="_self">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p3">(<span class="default"><font color="Maroon">D</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p4">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p5">(<span class="default"><font color="Maroon">C</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p0">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p1">(<span class="default"><font color="Maroon">D</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p2">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <font color="Maroon">C</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <span class="p2">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p3">(<span class="default"><font color="Maroon">D</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p4">(<span class="default"><font color="Maroon">C</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p5">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p0">(<span class="default"><font color="Maroon">D</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p1">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <font color="Maroon">C</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="lattices.html#D5">LATTICES:def 5</a></i>
<br/>.= 
<font color="Maroon">D</font>
<b>by </b><i/>
;<br/></div><b>end;</b></div>
<a NAME="E9:99"/><b>then </b><i><font color="Green">E76</font></i>: 
 <a href="robbins1.html#NK11" target="_self">-</a> <span class="p1">(<span class="default"><font color="Maroon">D</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p2">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">D</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p5">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <font color="Maroon">C</font></span>)</span></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <span class="p4">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p5">(<span class="default"><font color="Maroon">C</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p0">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p1">(<span class="default"><font color="Maroon">D</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p2">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <font color="Maroon">C</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="robbins1.html#NK11" target="_self">-</a> <span class="p1">(<span class="default"><font color="Maroon">C</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p2">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p3">(<span class="default"><font color="Maroon">D</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p4">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <font color="Maroon">C</font></span>)</span></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i/>;<br/>
<b>set </b><font color="Maroon">L</font> = <font color="Maroon">C</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p1">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p2">(<span class="default"><font color="Maroon">D</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p3">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <font color="Maroon">C</font></span>)</span></span>)</span></span>)</span>;<br/>
<i><font color="Green">E77</font></i>: <font color="Maroon">C</font> = 
 <a href="robbins1.html#NK11" target="_self">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">D</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p5">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p0">(<span class="default"><font color="Maroon">C</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p1">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p2">(<span class="default"><font color="Maroon">D</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p3">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <font color="Maroon">C</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">C</font></span>)</span></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <span class="p2">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p5">(<span class="default"><font color="Maroon">D</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p0">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <font color="Maroon">C</font></span>)</span></span>)</span></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">C</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="robbins1.html#T27" target="_self">Th27</a>, </i>
<br/>.= 
 <a href="robbins1.html#NK11" target="_self">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p3">(<span class="default"><font color="Maroon">C</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p4">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p5">(<span class="default"><font color="Maroon">D</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p0">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <font color="Maroon">C</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <span class="p2">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p3">(<span class="default"><font color="Maroon">C</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p4">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p5">(<span class="default"><font color="Maroon">C</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p0">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p1">(<span class="default"><font color="Maroon">D</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p2">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <font color="Maroon">C</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="lattices.html#D5">LATTICES:def 5</a></i>
;<br/>
<div><i><font color="Green">E78</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="99_7"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">G</font>;<br/><b>let </b><font color="Maroon">y</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">G</font>;<br/><b>let </b><font color="Maroon">z</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">G</font>;<br/><b>set </b><font color="Maroon">k</font> =  <a href="robbins1.html#NK11" target="_self">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <font color="Maroon">x</font></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">y</font></span>)</span>;<br/><a NAME="E1:99_7"/>
 <a href="robbins1.html#NK11" target="_self">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <font color="Maroon">x</font></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">x</font></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">y</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="robbins1.html#NK11" target="_self">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <font color="Maroon">x</font></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">y</font></span>)</span>
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E2:99_7"/>
<font color="Maroon">z</font> <a href="hidden.html#R1">=</a>  <a href="robbins1.html#NK11" target="_self">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <font color="Maroon">x</font></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">x</font></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">y</font></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <span class="p2">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <font color="Maroon">x</font></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">z</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i/>;<br/></div><b>end;</b></div>
<i><font color="Green">E79</font></i>:  <a href="robbins1.html#NK11" target="_self">-</a> <span class="p1">(<span class="default"><font color="Maroon">C</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p2">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p3">(<span class="default"><font color="Maroon">D</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p4">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <font color="Maroon">C</font></span>)</span></span>)</span></span>)</span></span>)</span> = 
 <a href="robbins1.html#NK11" target="_self">-</a> <span class="p1">(<span class="default"><font color="Maroon">D</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p2">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">D</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p5">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p0">(<span class="default"><font color="Maroon">C</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p1">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p2">(<span class="default"><font color="Maroon">D</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p3">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <font color="Maroon">C</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <span class="p4">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <font color="Maroon">C</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="robbins1.html#T28" target="_self">Th28</a>, <a class="ref" href="lattices.html#D5">LATTICES:def 5</a></i>
<br/>.= 
 <a href="robbins1.html#NK11" target="_self">-</a> <font color="Maroon">C</font>
<b>by </b><i>, <a class="ref" href="robbins1.html#T27" target="_self">Th27</a>, </i>
;<br/>
<a NAME="E13:99"/><b>then </b><i><font color="Green">E118</font></i>: 
 <a href="robbins1.html#NK11" target="_self">-</a> <span class="p1">(<span class="default"><font color="Maroon">C</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p2">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p3">(<span class="default"><font color="Maroon">C</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p4">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p5">(<span class="default"><font color="Maroon">C</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p0">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <font color="Maroon">C</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="robbins1.html#NK11" target="_self">-</a> <span class="p1">(<span class="default"><font color="Maroon">C</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p2">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <font color="Maroon">C</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="robbins1.html#T29" target="_self">Th29</a>, </i>;<br/>
<b>set </b><font color="Maroon">K</font> =  <a href="robbins1.html#NK11" target="_self">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">C</font> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">C</font></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <span class="p2">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p3">(<span class="default"><font color="Maroon">C</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p4">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <font color="Maroon">C</font></span>)</span></span>)</span></span>)</span></span>)</span>;<br/>
<a NAME="E14:99"/>
 <a href="robbins1.html#NK11" target="_self">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">C</font> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">C</font></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <span class="p2">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p3">(<span class="default"><font color="Maroon">C</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p4">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <font color="Maroon">C</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="robbins1.html#NK11" target="_self">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">C</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p3">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p4">(<span class="default"><font color="Maroon">C</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p5">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <font color="Maroon">C</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">C</font></span>)</span>
 
<b>by </b><i><a class="ref" href="lattices.html#D5">LATTICES:def 5</a></i>;<br/>
<a NAME="E15:99"/><b>then </b>
<font color="Maroon">C</font> <a href="hidden.html#R1">=</a>  <a href="robbins1.html#NK11" target="_self">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p3">(<span class="default"><font color="Maroon">C</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p4">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <font color="Maroon">C</font></span>)</span></span>)</span></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <span class="p2">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">C</font> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">C</font></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <span class="p4">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p5">(<span class="default"><font color="Maroon">C</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p0">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <font color="Maroon">C</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="robbins1.html#T30" target="_self">Th30</a>, </i>;<br/>
<a NAME="E16:99"/><b>then </b>
 <a href="robbins1.html#NK11" target="_self">-</a> <span class="p1">(<span class="default"><font color="Maroon">C</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p2">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">C</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p5">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <font color="Maroon">C</font></span>)</span></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <span class="p4">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">C</font> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">C</font></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <span class="p0">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p1">(<span class="default"><font color="Maroon">C</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p2">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <font color="Maroon">C</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="robbins1.html#NK11" target="_self">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">C</font> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">C</font></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <span class="p2">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p3">(<span class="default"><font color="Maroon">C</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p4">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <font color="Maroon">C</font></span>)</span></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i/>;<br/>
<b>then </b> <a href="robbins1.html#NK11" target="_self">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">C</font> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">C</font></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <span class="p2">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p3">(<span class="default"><font color="Maroon">C</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p4">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <font color="Maroon">C</font></span>)</span></span>)</span></span>)</span></span>)</span> = 
 <a href="robbins1.html#NK11" target="_self">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">C</font> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">C</font></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <span class="p1">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p2">(<span class="default"><font color="Maroon">C</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p3">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <font color="Maroon">C</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">C</font></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <span class="p4">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <font color="Maroon">C</font></span>)</span></span>)</span></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">C</font></span>)</span>
<b>by </b><i><a class="ref" href="lattices.html#D5">LATTICES:def 5</a></i>
<br/>.= 
 <a href="robbins1.html#NK11" target="_self">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p3">(<span class="default"><font color="Maroon">C</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p4">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <font color="Maroon">C</font></span>)</span></span>)</span></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">C</font></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">C</font></span>)</span></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">C</font></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <span class="p4">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <font color="Maroon">C</font></span>)</span></span>)</span></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">C</font></span>)</span>
<b>by </b><i><a class="ref" href="lattices.html#D5">LATTICES:def 5</a></i>
<br/>.= 
 <a href="robbins1.html#NK11" target="_self">-</a> <font color="Maroon">C</font>
<b>by </b><i><a class="ref" href="robbins1.html#T29" target="_self">Th29</a>, , </i>
;<br/>
<b>then </b><font color="Maroon">D</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p1">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p2">(<span class="default"><font color="Maroon">C</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p3">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <font color="Maroon">C</font></span>)</span></span>)</span></span>)</span> = 
 <a href="robbins1.html#NK11" target="_self">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">D</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p5">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p0">(<span class="default"><font color="Maroon">C</font> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">C</font></span>)</span></span>)</span></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <span class="p4">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p5">(<span class="default"><font color="Maroon">C</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p0">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <font color="Maroon">C</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <span class="p2">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <font color="Maroon">C</font></span>)</span></span>)</span>
<b>by </b><i/>
<br/>.= 
 <a href="robbins1.html#NK11" target="_self">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <font color="Maroon">C</font></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <span class="p2">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">D</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p5">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p0">(<span class="default"><font color="Maroon">C</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p1">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <font color="Maroon">C</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <span class="p4">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p5">(<span class="default"><font color="Maroon">C</font> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">C</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="lattices.html#D5">LATTICES:def 5</a></i>
<br/>.= 
<font color="Maroon">D</font>
<b>by </b><i><a class="ref" href="robbins1.html#T26" target="_self">Th26</a></i>
;<br/>
<a NAME="E19:99"/><b>then </b><i><font color="Green">E122</font></i>: 
<font color="Maroon">C</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p1">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p2">(<span class="default"><font color="Maroon">C</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p3">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <font color="Maroon">C</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">C</font>
 
<b>by </b><i>, <a class="ref" href="lattices.html#D5">LATTICES:def 5</a></i>;<br/>
<div><i><font color="Green">E123</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="99_11"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">G</font>;<br/><b>thus </b><font color="Maroon">x</font> = 
 <a href="robbins1.html#NK11" target="_self">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">C</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p5">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p0">(<span class="default"><font color="Maroon">C</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p1">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <font color="Maroon">C</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <span class="p2">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <font color="Maroon">C</font></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <span class="p5">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p0">(<span class="default"><font color="Maroon">C</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p1">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <font color="Maroon">C</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="robbins1.html#T29" target="_self">Th29</a>, , , </i>
<br/>.= 
 <a href="robbins1.html#NK11" target="_self">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p3">(<span class="default"><font color="Maroon">C</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p0">(<span class="default"><font color="Maroon">C</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p1">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <font color="Maroon">C</font></span>)</span></span>)</span></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <span class="p2">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <font color="Maroon">C</font></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <span class="p5">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p0">(<span class="default"><font color="Maroon">C</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p1">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <font color="Maroon">C</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="lattices.html#D5">LATTICES:def 5</a></i>
<br/>.= 
 <a href="robbins1.html#NK11" target="_self">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p3">(<span class="default"><font color="Maroon">C</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p0">(<span class="default"><font color="Maroon">C</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p1">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <font color="Maroon">C</font></span>)</span></span>)</span></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <span class="p2">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <font color="Maroon">C</font></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p0">(<span class="default"><font color="Maroon">C</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p1">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <font color="Maroon">C</font></span>)</span></span>)</span></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="lattices.html#D5">LATTICES:def 5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p2">(<span class="default"><font color="Maroon">C</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p3">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <font color="Maroon">C</font></span>)</span></span>)</span></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">x</font>
<b>by </b><i/>
;<br/></div><b>end;</b></div>
<b>set </b><font color="Maroon">e</font> =  <a href="robbins1.html#NK11" target="_self">-</a> <span class="p1">(<span class="default"><font color="Maroon">C</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p2">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <font color="Maroon">C</font></span>)</span></span>)</span>;<br/>
<a NAME="E21:99"/>
 <a href="robbins1.html#NK11" target="_self">-</a> <span class="p1">(<span class="default"><font color="Maroon">C</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p2">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <font color="Maroon">C</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p2">(<span class="default"><font color="Maroon">C</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p3">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <font color="Maroon">C</font></span>)</span></span>)</span></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <span class="p1">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <span class="p2">(<span class="default"><font color="Maroon">C</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p3">(<span class="default"><a href="robbins1.html#NK11" target="_self">-</a> <font color="Maroon">C</font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="robbins1.html#E5:99"><i><font color="Green">E73</font></i></a></i>;<br/>
<a NAME="E22:99"/><b>then </b>
<font color="Maroon">G</font> is <a href="robbins1.html#V8" target="_self">with_idempotent_element</a>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E23:99"/>
<font color="Maroon">G</font> is <a href="robbins1.html#V5" target="_self">Huntington</a>
 <b>by </b><i/>;<br/>


</div>
