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

<b>let </b><font color="Maroon" title="c1">G</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a> <a href="lattices.html#V4" title="LATTICES:attr.4">join-commutative</a> <a href="lattices.html#V5" title="LATTICES:attr.5">join-associative</a> <a href="robbins1.html#V4" title="ROBBINS1:attr.4">Robbins</a>  <a href="robbins1.html#L2" title="ROBBINS1:struct.2">ComplLattStr</a> ;<br/>

<b>assume </b><a NAME="E1:96"/>
<font color="Maroon" title="c1">G</font> is <a href="robbins1.html#V8" title="ROBBINS1:attr.8">with_idempotent_element</a>
 ;<br/>

<b>then consider </b><font color="Maroon" title="c2">C</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">G</font><b> such that </b><br/><a NAME="E3:96"/><i><font color="Green" title="E59">A1</font></i>: 
<font color="Maroon" title="c2">C</font> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <font color="Maroon" title="c2">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">C</font>
 <b>by </b><i><a class="ref" href="robbins1.html#D13" target="_self" title="ROBBINS1:def.13">Def13</a></i>;<br/>
<b>assume </b><a NAME="E4:96"/>
not <font color="Maroon" title="c1">G</font> is <a href="robbins1.html#V5" title="ROBBINS1:attr.5">Huntington</a>
 ;<br/>

<b>then consider </b><font color="Maroon" title="c3">B</font>, <font color="Maroon" title="c4">A</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">G</font><b> such that </b><br/><a NAME="E6:96"/><i><font color="Green" title="E60">A2</font></i>: 
<span class="p1">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c3">B</font></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p3">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c4">A</font></span>)</span></span>)</span></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p1">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">B</font> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p3">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c4">A</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">A</font>
 <b>by </b><i><a class="ref" href="robbins1.html#D12" target="_self" title="ROBBINS1:def.12">Def12</a></i>;<br/>
<a NAME="E7:96"/><i><font color="Green" title="E61">A3</font></i>: 
<font color="Maroon" title="c2">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c2">C</font></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p2">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">C</font> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p4">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c2">C</font></span>)</span></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="robbins1.html#E3:96"><i><font color="Green" title="E59">A1</font></i></a>, <a class="ref" href="robbins1.html#D5" target="_self" title="ROBBINS1:def.5">Def5</a></i>;<br/>
<div><i><font color="Green" title="E62">A4</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="96_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c5">x</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">G</font>;<br/><b>thus </b><font color="Maroon" title="c2">C</font> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <font color="Maroon" title="c5">x</font> = 
 <a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c2">C</font></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">C</font> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <font color="Maroon" title="c5">x</font></span>)</span></span>)</span></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p2">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">C</font> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">C</font> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <font color="Maroon" title="c5">x</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="robbins1.html#D5" target="_self" title="ROBBINS1:def.5">Def5</a></i>
<br/>.= 
 <a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c2">C</font></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <font color="Maroon" title="c2">C</font></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <font color="Maroon" title="c5">x</font></span>)</span></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p2">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">C</font> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">C</font> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <font color="Maroon" title="c5">x</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="lattices.html#D5" title="LATTICES:def.5">LATTICES:def 5</a></i>
<br/>.= 
 <a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">C</font> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p5">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c2">C</font></span>)</span></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <font color="Maroon" title="c5">x</font></span>)</span></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p2">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">C</font> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <font color="Maroon" title="c5">x</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="robbins1.html#E3:96"><i><font color="Green" title="E59">A1</font></i></a>, <a class="ref" href="lattices.html#D5" title="LATTICES:def.5">LATTICES:def 5</a></i>
;<br/></div><b>end;</b></div>
<a NAME="E9:96"/><i><font color="Green" title="E63">A5</font></i>: 
 <a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">C</font> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p2">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">C</font> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p5">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c2">C</font></span>)</span></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p4">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c2">C</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c2">C</font>
 
<b>by </b><i><a class="txt" href="robbins1.html#E7:96"><i><font color="Green" title="E61">A3</font></i></a>, <a class="ref" href="robbins1.html#D5" target="_self" title="ROBBINS1:def.5">Def5</a></i>;<br/>
<i><font color="Green" title="E64">A6</font></i>: <font color="Maroon" title="c2">C</font> = 
 <a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">C</font> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <font color="Maroon" title="c2">C</font></span>)</span></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p2">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c2">C</font></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p5">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p0">(<span class="default"><font color="Maroon" title="c2">C</font> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p1">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c2">C</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <font color="Maroon" title="c2">C</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="robbins1.html#E7:96"><i><font color="Green" title="E61">A3</font></i></a>, <a class="ref" href="robbins1.html#D5" target="_self" title="ROBBINS1:def.5">Def5</a></i>
<br/>.= 
 <a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c2">C</font></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p2">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">C</font> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p5">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c2">C</font></span>)</span></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p4">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p5">(<span class="default"><font color="Maroon" title="c2">C</font> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p0">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c2">C</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="robbins1.html#E3:96"><i><font color="Green" title="E59">A1</font></i></a>, <a class="ref" href="lattices.html#D5" title="LATTICES:def.5">LATTICES:def 5</a></i>
;<br/>
<b>set </b><font color="Maroon" title="c5">D</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c2">C</font> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p2">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c2">C</font></span>)</span></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p1">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c2">C</font></span>)</span>;<br/>
 <a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c2">C</font></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p2">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">C</font> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p5">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c2">C</font></span>)</span></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p4">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c2">C</font></span>)</span></span>)</span></span>)</span></span>)</span> = 
 <a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c2">C</font> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p1">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c2">C</font></span>)</span></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p0">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c2">C</font></span>)</span></span>)</span></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <font color="Maroon" title="c2">C</font></span>)</span></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p2">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">C</font> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <font color="Maroon" title="c2">C</font></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c2">C</font></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p5">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c2">C</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="robbins1.html#E3:96"><i><font color="Green" title="E59">A1</font></i></a>, <a class="txt" href="robbins1.html#E9:96"><i><font color="Green" title="E63">A5</font></i></a>, <a class="ref" href="lattices.html#D5" title="LATTICES:def.5">LATTICES:def 5</a></i>
<br/>.= 
 <a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c2">C</font> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p1">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c2">C</font></span>)</span></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p0">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c2">C</font></span>)</span></span>)</span></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <font color="Maroon" title="c2">C</font></span>)</span></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p2">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">C</font> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">C</font> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c2">C</font></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p0">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c2">C</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="lattices.html#D5" title="LATTICES:def.5">LATTICES:def 5</a></i>
<br/>.= 
 <a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c2">C</font> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p1">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c2">C</font></span>)</span></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p0">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c2">C</font></span>)</span></span>)</span></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <font color="Maroon" title="c2">C</font></span>)</span></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p2">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c2">C</font> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p0">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c2">C</font></span>)</span></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p5">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c2">C</font></span>)</span></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <font color="Maroon" title="c2">C</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="lattices.html#D5" title="LATTICES:def.5">LATTICES:def 5</a></i>
<br/>.= 
<font color="Maroon" title="c2">C</font>
<b>by </b><i><a class="ref" href="robbins1.html#D5" target="_self" title="ROBBINS1:def.5">Def5</a></i>
;<br/>
<a NAME="E12:96"/><b>then </b>
 <a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">C</font> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p2">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c2">C</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">C</font> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p3">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c2">C</font></span>)</span></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p2">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c2">C</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="robbins1.html#E9:96"><i><font color="Green" title="E63">A5</font></i></a>, <a class="ref" href="robbins1.html#D5" target="_self" title="ROBBINS1:def.5">Def5</a></i>;<br/>
<a NAME="E13:96"/><b>then </b><i><font color="Green" title="E65">A7</font></i>: 
<font color="Maroon" title="c2">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">C</font> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p1">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">C</font> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p3">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c2">C</font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="robbins1.html#E8:96"><i><font color="Green" title="E62">A4</font></i></a>, <a class="txt" href="robbins1.html#E9:96"><i><font color="Green" title="E63">A5</font></i></a>, <a class="txt" href="robbins1.html#E10:96"><i><font color="Green" title="E64">A6</font></i></a></i>;<br/>
<div><i><font color="Green" title="E66">A8</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="96_4"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c6">x</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">G</font>;<br/><b>thus </b><font color="Maroon" title="c6">x</font> = 
 <a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">C</font> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p5">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p0">(<span class="default"><font color="Maroon" title="c2">C</font> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p1">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c2">C</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <font color="Maroon" title="c6">x</font></span>)</span></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p2">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c2">C</font></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p5">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p0">(<span class="default"><font color="Maroon" title="c2">C</font> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p1">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c2">C</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <font color="Maroon" title="c6">x</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="robbins1.html#E7:96"><i><font color="Green" title="E61">A3</font></i></a>, <a class="txt" href="robbins1.html#E13:96"><i><font color="Green" title="E65">A7</font></i></a>, <a class="ref" href="robbins1.html#D5" target="_self" title="ROBBINS1:def.5">Def5</a></i>
<br/>.= 
 <a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">C</font> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p0">(<span class="default"><font color="Maroon" title="c2">C</font> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p1">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c2">C</font></span>)</span></span>)</span></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <font color="Maroon" title="c6">x</font></span>)</span></span>)</span></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p2">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c2">C</font></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p5">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p0">(<span class="default"><font color="Maroon" title="c2">C</font> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p1">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c2">C</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <font color="Maroon" title="c6">x</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="lattices.html#D5" title="LATTICES:def.5">LATTICES:def 5</a></i>
<br/>.= 
 <a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">C</font> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p0">(<span class="default"><font color="Maroon" title="c2">C</font> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p1">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c2">C</font></span>)</span></span>)</span></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <font color="Maroon" title="c6">x</font></span>)</span></span>)</span></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p2">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c2">C</font></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p0">(<span class="default"><font color="Maroon" title="c2">C</font> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p1">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c2">C</font></span>)</span></span>)</span></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <font color="Maroon" title="c6">x</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="lattices.html#D5" title="LATTICES:def.5">LATTICES:def 5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">C</font> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p3">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c2">C</font></span>)</span></span>)</span></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <font color="Maroon" title="c6">x</font>
<b>by </b><i><a class="ref" href="robbins1.html#D5" target="_self" title="ROBBINS1:def.5">Def5</a></i>
;<br/></div><b>end;</b></div>
<div><i><font color="Green" title="E67">A9</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="96_5"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c6">x</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">G</font>;<br/><b>thus </b> <a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">C</font> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p2">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c2">C</font></span>)</span></span>)</span> = 
 <a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c6">x</font></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p4">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p5">(<span class="default"><font color="Maroon" title="c2">C</font> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p0">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c2">C</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p2">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">x</font> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p4">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p5">(<span class="default"><font color="Maroon" title="c2">C</font> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p0">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c2">C</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="robbins1.html#D5" target="_self" title="ROBBINS1:def.5">Def5</a></i>
<br/>.= 
 <a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p3">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c6">x</font></span>)</span></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p2">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">x</font> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p4">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p5">(<span class="default"><font color="Maroon" title="c2">C</font> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p0">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c2">C</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="robbins1.html#E14:96"><i><font color="Green" title="E66">A8</font></i></a></i>
<br/>.= 
 <a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p3">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c6">x</font></span>)</span></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p2">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c6">x</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="robbins1.html#E14:96"><i><font color="Green" title="E66">A8</font></i></a></i>
;<br/></div><b>end;</b></div>
<div><i><font color="Green" title="E68">A10</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="96_6"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c6">x</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">G</font>;<br/><b>thus </b> <a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p1">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c6">x</font></span>)</span> = 
 <a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c6">x</font></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p4">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p5">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c6">x</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p2">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">x</font> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p4">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p5">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c6">x</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="robbins1.html#D5" target="_self" title="ROBBINS1:def.5">Def5</a></i>
<br/>.= 
 <a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">C</font> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p4">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c2">C</font></span>)</span></span>)</span></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p2">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">x</font> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p4">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p5">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c6">x</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="robbins1.html#E15:96"><i><font color="Green" title="E67">A9</font></i></a></i>
<br/>.= 
 <a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p1">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">x</font> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p3">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p4">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c6">x</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="robbins1.html#E14:96"><i><font color="Green" title="E66">A8</font></i></a></i>
;<br/></div><b>end;</b></div>
<div><i><font color="Green" title="E69">A11</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="96_7"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c6">x</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">G</font>;<br/><b>thus </b> <a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c6">x</font> = 
 <a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p5">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p0">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c6">x</font></span>)</span></span>)</span></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p4">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c6">x</font></span>)</span></span>)</span></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p2">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p5">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c6">x</font></span>)</span></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p4">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c6">x</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="robbins1.html#D5" target="_self" title="ROBBINS1:def.5">Def5</a></i>
<br/>.= 
 <a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p5">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p0">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c6">x</font></span>)</span></span>)</span></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p4">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c6">x</font></span>)</span></span>)</span></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p2">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">C</font> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p4">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c2">C</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="robbins1.html#E15:96"><i><font color="Green" title="E67">A9</font></i></a></i>
<br/>.= 
 <a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p1">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p4">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p5">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c6">x</font></span>)</span></span>)</span></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p3">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c6">x</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="robbins1.html#E14:96"><i><font color="Green" title="E66">A8</font></i></a></i>
<br/>.= 
 <a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p1">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p2">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c6">x</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="robbins1.html#E16:96"><i><font color="Green" title="E68">A10</font></i></a></i>
;<br/></div><b>end;</b></div>
<div><i><font color="Green" title="E70">A12</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="96_8"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c6">x</font>, <font color="Maroon" title="c7">y</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">G</font>;<br/><b>thus </b><font color="Maroon" title="c7">y</font> = 
 <a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c6">x</font></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <font color="Maroon" title="c7">y</font></span>)</span></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p2">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">x</font> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <font color="Maroon" title="c7">y</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="robbins1.html#D5" target="_self" title="ROBBINS1:def.5">Def5</a></i>
<br/>.= 
 <a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p1">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p2">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c6">x</font></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <font color="Maroon" title="c7">y</font></span>)</span></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p4">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p5">(<span class="default"><font color="Maroon" title="c6">x</font> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <font color="Maroon" title="c7">y</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="robbins1.html#E17:96"><i><font color="Green" title="E69">A11</font></i></a></i>
<br/>.= 
 <a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p1">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c7">y</font></span>)</span>
<b>by </b><i><a class="ref" href="robbins1.html#D5" target="_self" title="ROBBINS1:def.5">Def5</a></i>
;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="96_9"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c6">x</font>, <font color="Maroon" title="c7">y</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">G</font>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c6">x</font></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <font color="Maroon" title="c7">y</font></span>)</span></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p1">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">x</font> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <font color="Maroon" title="c7">y</font></span>)</span></span>)</span> = 
 <a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p1">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c6">x</font></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <font color="Maroon" title="c7">y</font></span>)</span></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p3">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c6">x</font> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <font color="Maroon" title="c7">y</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="robbins1.html#E18:96"><i><font color="Green" title="E70">A12</font></i></a></i>
<br/>.= 
 <a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c7">y</font>
<b>by </b><i><a class="ref" href="robbins1.html#D5" target="_self" title="ROBBINS1:def.5">Def5</a></i>
;<br/></div><b>end;</b></div>
<b>then </b><span class="p1">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c3">B</font></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p3">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c4">A</font></span>)</span></span>)</span></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p1">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">B</font> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p3">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c4">A</font></span>)</span></span>)</span></span>)</span> = 
 <a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p1">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c4">A</font></span>)</span>

<br/>.= 
<font color="Maroon" title="c4">A</font>
<b>by </b><i><a class="txt" href="robbins1.html#E18:96"><i><font color="Green" title="E70">A12</font></i></a></i>
;<br/>
<b>hence </b><a NAME="E21:96"/>
contradiction
 <b>by </b><i><a class="txt" href="robbins1.html#E6:96"><i><font color="Green" title="E60">A2</font></i></a></i>;<br/>


</div>
