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

<span class="kw">let </span><font color="Maroon" title="c1">G</font> be  non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">G</font> is  <a href="robbins1.html#V8" title="ROBBINS1:attr.8">with_idempotent_element</a>  implies <font color="Maroon" title="c1">G</font> is  <a href="robbins1.html#V5" title="ROBBINS1:attr.5">Huntington</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:97"/>
<font color="Maroon" title="c1">G</font> is  <a href="robbins1.html#V8" title="ROBBINS1:attr.8">with_idempotent_element</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">G</font> is  <a href="robbins1.html#V5" title="ROBBINS1:attr.5">Huntington</a> </span><br/>

<span class="kw">then </span><span class="kw">consider </span><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><span class="kw"> such that </span><br/><a NAME="E3:97"/><span class="lab"><font color="Green" title="E56">A1</font></span>: 
<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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="robbins1.html#D13" target="_self" title="ROBBINS1:def.13">Def13</a></span>;<br/>
<div><span class="lab"><font color="Green" title="E57">A2</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="97_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c3">x</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">G</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">C</font> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <font color="Maroon" title="c3">x</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> <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="c3">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="c3">x</font></span>)</span></span>)</span></span>)</span></span><br/><span class="kw">thus </span><font color="Maroon" title="c2">C</font> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <font color="Maroon" title="c3">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="c3">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="c3">x</font></span>)</span></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="robbins1.html#D5" target="_self" title="ROBBINS1:def.5">Def5</a></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> <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="c3">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="c3">x</font></span>)</span></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="lattices.html#D5" title="LATTICES:def.5">LATTICES:def 5</a></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> <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="c3">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="c3">x</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:97"><span class="lab"><font color="Green" title="E56">A1</font></span></a>, <a class="ref" href="lattices.html#D5" title="LATTICES:def.5">LATTICES:def 5</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">assume </span><a NAME="E5:97"/>
not <font color="Maroon" title="c1">G</font> is  <a href="robbins1.html#V5" title="ROBBINS1:attr.5">Huntington</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<span class="kw">then </span><span class="kw">consider </span><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><span class="kw"> such that </span><br/><a NAME="E7:97"/><span class="lab"><font color="Green" title="E58">A3</font></span>: 
<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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="robbins1.html#D12" target="_self" title="ROBBINS1:def.12">Def12</a></span>;<br/>
<span class="kw">set </span><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 NAME="E8:97"/><span class="lab"><font color="Green" title="E59">A4</font></span>: 
<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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:97"><span class="lab"><font color="Green" title="E56">A1</font></span></a>, <a class="ref" href="robbins1.html#D5" target="_self" title="ROBBINS1:def.5">Def5</a></span>;<br/>
<a NAME="E9:97"/><span class="kw">then </span><span class="lab"><font color="Green" title="E60">A5</font></span>: 
 <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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="robbins1.html#D5" target="_self" title="ROBBINS1:def.5">Def5</a></span>;<br/>
<span class="kw">then </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> <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>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:97"><span class="lab"><font color="Green" title="E56">A1</font></span></a>, <a class="ref" href="lattices.html#D5" title="LATTICES:def.5">LATTICES:def 5</a></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> <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>
<span class="kw">by</span> <span class="lab"><a class="ref" href="lattices.html#D5" title="LATTICES:def.5">LATTICES:def 5</a></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> <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>
<span class="kw">by</span> <span class="lab"><a class="ref" href="lattices.html#D5" title="LATTICES:def.5">LATTICES:def 5</a></span>
<br/>.= 
<font color="Maroon" title="c2">C</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="robbins1.html#D5" target="_self" title="ROBBINS1:def.5">Def5</a></span>
;<br/>
<a NAME="E11:97"/><span class="kw">then </span><span class="lab"><font color="Green" title="E61">A6</font></span>: 
 <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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:97"><span class="lab"><font color="Green" title="E60">A5</font></span></a>, <a class="ref" href="robbins1.html#D5" target="_self" title="ROBBINS1:def.5">Def5</a></span>;<br/>
<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>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:97"><span class="lab"><font color="Green" title="E59">A4</font></span></a>, <a class="ref" href="robbins1.html#D5" target="_self" title="ROBBINS1:def.5">Def5</a></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> <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>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:97"><span class="lab"><font color="Green" title="E56">A1</font></span></a>, <a class="ref" href="lattices.html#D5" title="LATTICES:def.5">LATTICES:def 5</a></span>
;<br/>
<a NAME="E13:97"/><span class="kw">then </span><span class="lab"><font color="Green" title="E62">A7</font></span>: 
<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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:97"><span class="lab"><font color="Green" title="E57">A2</font></span></a>, <a class="txt" href="#E9:97"><span class="lab"><font color="Green" title="E60">A5</font></span></a>, <a class="txt" href="#E11:97"><span class="lab"><font color="Green" title="E61">A6</font></span></a></span>;<br/>
<div><span class="lab"><font color="Green" title="E63">A8</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="97_4"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><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>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c6">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <font color="Maroon" title="c6">x</font></span><br/><span class="kw">thus </span><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>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:97"><span class="lab"><font color="Green" title="E59">A4</font></span></a>, <a class="txt" href="#E13:97"><span class="lab"><font color="Green" title="E62">A7</font></span></a>, <a class="ref" href="robbins1.html#D5" target="_self" title="ROBBINS1:def.5">Def5</a></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> <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>
<span class="kw">by</span> <span class="lab"><a class="ref" href="lattices.html#D5" title="LATTICES:def.5">LATTICES:def 5</a></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> <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>
<span class="kw">by</span> <span class="lab"><a class="ref" href="lattices.html#D5" title="LATTICES:def.5">LATTICES:def 5</a></span>
<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>
<span class="kw">by</span> <span class="lab"><a class="ref" href="robbins1.html#D5" target="_self" title="ROBBINS1:def.5">Def5</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<div><span class="lab"><font color="Green" title="E64">A9</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="97_5"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><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>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <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"><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></span><br/><span class="kw">thus </span> <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>
<span class="kw">by</span> <span class="lab"><a class="ref" href="robbins1.html#D5" target="_self" title="ROBBINS1:def.5">Def5</a></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> <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>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:97"><span class="lab"><font color="Green" title="E63">A8</font></span></a></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> <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>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:97"><span class="lab"><font color="Green" title="E63">A8</font></span></a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<div><span class="lab"><font color="Green" title="E65">A10</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="97_6"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><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>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <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="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <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></span><br/><span class="kw">thus </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="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>
<span class="kw">by</span> <span class="lab"><a class="ref" href="robbins1.html#D5" target="_self" title="ROBBINS1:def.5">Def5</a></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> <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>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:97"><span class="lab"><font color="Green" title="E64">A9</font></span></a></span>
<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>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:97"><span class="lab"><font color="Green" title="E63">A8</font></span></a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<div><span class="lab"><font color="Green" title="E66">A11</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="97_7"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><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>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c6">x</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"><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></span><br/><span class="kw">thus </span> <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>
<span class="kw">by</span> <span class="lab"><a class="ref" href="robbins1.html#D5" target="_self" title="ROBBINS1:def.5">Def5</a></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> <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>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:97"><span class="lab"><font color="Green" title="E64">A9</font></span></a></span>
<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>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:97"><span class="lab"><font color="Green" title="E63">A8</font></span></a></span>
<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>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:97"><span class="lab"><font color="Green" title="E65">A10</font></span></a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<div><span class="lab"><font color="Green" title="E67">A12</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="97_8"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><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>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c7">y</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"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c7">y</font></span>)</span></span><br/><span class="kw">thus </span><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>
<span class="kw">by</span> <span class="lab"><a class="ref" href="robbins1.html#D5" target="_self" title="ROBBINS1:def.5">Def5</a></span>
<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>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:97"><span class="lab"><font color="Green" title="E66">A11</font></span></a></span>
<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>
<span class="kw">by</span> <span class="lab"><a class="ref" href="robbins1.html#D5" target="_self" title="ROBBINS1:def.5">Def5</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="97_9"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><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>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><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="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c7">y</font></span><br/><span class="kw">thus </span><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>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E18:97"><span class="lab"><font color="Green" title="E67">A12</font></span></a></span>
<br/>.= 
 <a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c7">y</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="robbins1.html#D5" target="_self" title="ROBBINS1:def.5">Def5</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">then </span><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>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E18:97"><span class="lab"><font color="Green" title="E67">A12</font></span></a></span>
;<br/>
<span class="kw">hence </span><a NAME="E21:97"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:97"><span class="lab"><font color="Green" title="E58">A3</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
