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<b>let </b><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> ;<br/><b>let </b><font color="Maroon" title="c2">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/>



<font color="Maroon" title="c2">x</font> = 
 <a href="robbins1.html#K10" title="ROBBINS1:func.10">Expand</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">x</font> <a href="robbins1.html#K15" title="ROBBINS1:func.15">_3</a> </span>)</span></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="robbins1.html#K11" title="ROBBINS1:func.11">_0</a> </span>)</span></span>)</span>,<font color="Maroon" title="c2">x</font>
<b>by </b><i><a class="ref" href="robbins1.html#T37" target="_self" title="ROBBINS1:th.37">Th37</a></i>
<br/>.= 
 <a href="robbins1.html#K9" title="ROBBINS1:func.9">\delta</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">x</font> <a href="robbins1.html#K15" title="ROBBINS1:func.15">_3</a> </span>)</span></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="robbins1.html#K13" title="ROBBINS1:func.13">_1</a> </span>)</span></span>)</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#K9" title="ROBBINS1:func.9">\delta</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="robbins1.html#K15" title="ROBBINS1:func.15">_3</a> </span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="robbins1.html#K11" title="ROBBINS1:func.11">_0</a> </span>)</span></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <font color="Maroon" title="c2">x</font></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#K9" title="ROBBINS1:func.9">\delta</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">x</font> <a href="robbins1.html#K15" title="ROBBINS1:func.15">_3</a> </span>)</span></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="robbins1.html#K13" title="ROBBINS1:func.13">_1</a> </span>)</span></span>)</span>,<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#K12" title="ROBBINS1:func.12">Double</a> <font color="Maroon" title="c2">x</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="robbins1.html#T47" target="_self" title="ROBBINS1:th.47">Th47</a></i>
;<br/>
<a NAME="E2:87"/><b>then </b><i><font color="Green" title="E50">A1</font></i>: 
 <a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p1">(<span class="default"><a href="robbins1.html#K12" title="ROBBINS1:func.12">Double</a> <font color="Maroon" title="c2">x</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="robbins1.html#K9" title="ROBBINS1:func.9">\delta</a> <span class="p1">(<span class="default"><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"><font color="Maroon" title="c2">x</font> <a href="robbins1.html#K15" title="ROBBINS1:func.15">_3</a> </span>)</span></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="robbins1.html#K13" title="ROBBINS1:func.13">_1</a> </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"><a href="robbins1.html#K12" title="ROBBINS1:func.12">Double</a> <font color="Maroon" title="c2">x</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c2">x</font>
 
<b>by </b><i><a class="ref" href="robbins1.html#T37" target="_self" title="ROBBINS1:th.37">Th37</a></i>;<br/>
<b>set </b><font color="Maroon" title="c3">alpha</font> = <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">x</font> <a href="robbins1.html#K15" title="ROBBINS1:func.15">_3</a> </span>)</span></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="robbins1.html#K13" title="ROBBINS1:func.13">_1</a> </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"><a href="robbins1.html#K12" title="ROBBINS1:func.12">Double</a> <font color="Maroon" title="c2">x</font></span>)</span></span>)</span>;<br/>
<i><font color="Green" title="E51">A2</font></i>: <font color="Maroon" title="c2">x</font> = 
 <a href="robbins1.html#K9" title="ROBBINS1:func.9">\delta</a> <span class="p1">(<span class="default"><a href="robbins1.html#K12" title="ROBBINS1:func.12">Double</a> <font color="Maroon" title="c2">x</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="robbins1.html#K11" title="ROBBINS1:func.11">_0</a> </span>)</span>
<b>by </b><i><a class="ref" href="robbins1.html#T41" target="_self" title="ROBBINS1:th.41">Th41</a></i>
<br/>.= 
 <a href="robbins1.html#K9" title="ROBBINS1:func.9">\delta</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> <span class="p0">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="robbins1.html#K15" title="ROBBINS1:func.15">_3</a> </span>)</span></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p5">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="robbins1.html#K13" title="ROBBINS1:func.13">_1</a> </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"><a href="robbins1.html#K12" title="ROBBINS1:func.12">Double</a> <font color="Maroon" title="c2">x</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <font color="Maroon" title="c2">x</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="robbins1.html#K11" title="ROBBINS1:func.11">_0</a> </span>)</span>
<b>by </b><i><a class="txt" href="robbins1.html#E2:87"><i><font color="Green" title="E50">A1</font></i></a></i>
;<br/>
 <a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="robbins1.html#K15" title="ROBBINS1:func.15">_3</a> </span>)</span> = 
 <a href="robbins1.html#K10" title="ROBBINS1:func.10">Expand</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="robbins1.html#K13" title="ROBBINS1:func.13">_1</a> </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"><a href="robbins1.html#K12" title="ROBBINS1:func.12">Double</a> <font color="Maroon" title="c2">x</font></span>)</span></span>)</span></span>)</span>,<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">x</font> <a href="robbins1.html#K15" title="ROBBINS1:func.15">_3</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="robbins1.html#T37" target="_self" title="ROBBINS1:th.37">Th37</a></i>
<br/>.= 
 <a href="robbins1.html#K9" title="ROBBINS1:func.9">\delta</a> <span class="p1">(<span class="default"><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"><font color="Maroon" title="c2">x</font> <a href="robbins1.html#K15" title="ROBBINS1:func.15">_3</a> </span>)</span></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="robbins1.html#K13" title="ROBBINS1:func.13">_1</a> </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"><a href="robbins1.html#K12" title="ROBBINS1:func.12">Double</a> <font color="Maroon" title="c2">x</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="robbins1.html#K9" title="ROBBINS1:func.9">\delta</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="robbins1.html#K13" title="ROBBINS1:func.13">_1</a> </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"><a href="robbins1.html#K12" title="ROBBINS1:func.12">Double</a> <font color="Maroon" title="c2">x</font></span>)</span></span>)</span></span>)</span>,<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">x</font> <a href="robbins1.html#K15" title="ROBBINS1:func.15">_3</a> </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#K9" title="ROBBINS1:func.9">\delta</a> <span class="p1">(<span class="default"><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"><font color="Maroon" title="c2">x</font> <a href="robbins1.html#K15" title="ROBBINS1:func.15">_3</a> </span>)</span></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="robbins1.html#K13" title="ROBBINS1:func.13">_1</a> </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"><a href="robbins1.html#K12" title="ROBBINS1:func.12">Double</a> <font color="Maroon" title="c2">x</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="robbins1.html#K9" title="ROBBINS1:func.9">\delta</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="robbins1.html#K11" title="ROBBINS1:func.11">_0</a> </span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p4">(<span class="default"><a href="robbins1.html#K12" title="ROBBINS1:func.12">Double</a> <font color="Maroon" title="c2">x</font></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="robbins1.html#K9" title="ROBBINS1:func.9">\delta</a> <span class="p3">(<span class="default"><a href="robbins1.html#K12" title="ROBBINS1:func.12">Double</a> <font color="Maroon" title="c2">x</font></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="robbins1.html#K13" title="ROBBINS1:func.13">_1</a> </span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="robbins1.html#T49" target="_self" title="ROBBINS1:th.49">Th49</a></i>
<br/>.= 
 <a href="robbins1.html#K9" title="ROBBINS1:func.9">\delta</a> <span class="p1">(<span class="default"><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"><font color="Maroon" title="c2">x</font> <a href="robbins1.html#K15" title="ROBBINS1:func.15">_3</a> </span>)</span></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="robbins1.html#K13" title="ROBBINS1:func.13">_1</a> </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"><a href="robbins1.html#K12" title="ROBBINS1:func.12">Double</a> <font color="Maroon" title="c2">x</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="robbins1.html#K9" title="ROBBINS1:func.9">\delta</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="robbins1.html#K12" title="ROBBINS1:func.12">Double</a> <font color="Maroon" title="c2">x</font></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="robbins1.html#K13" title="ROBBINS1:func.13">_1</a> </span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="robbins1.html#K9" title="ROBBINS1:func.9">\delta</a> <span class="p3">(<span class="default"><a href="robbins1.html#K12" title="ROBBINS1:func.12">Double</a> <font color="Maroon" title="c2">x</font></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="robbins1.html#K13" title="ROBBINS1:func.13">_1</a> </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"><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">x</font> <a href="robbins1.html#K15" title="ROBBINS1:func.15">_3</a> </span>)</span></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p5">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="robbins1.html#K13" title="ROBBINS1:func.13">_1</a> </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"><a href="robbins1.html#K12" title="ROBBINS1:func.12">Double</a> <font color="Maroon" title="c2">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"><font color="Maroon" title="c2">x</font> <a href="robbins1.html#K13" title="ROBBINS1:func.13">_1</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="robbins1.html#T37" target="_self" title="ROBBINS1:th.37">Th37</a></i>
;<br/>
<b>hence </b> <a href="robbins1.html#K9" title="ROBBINS1:func.9">\delta</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="robbins1.html#K15" title="ROBBINS1:func.15">_3</a> </span>)</span>,<font color="Maroon" title="c2">x</font> = 
 <a href="robbins1.html#K9" title="ROBBINS1:func.9">\delta</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> <span class="p0">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="robbins1.html#K15" title="ROBBINS1:func.15">_3</a> </span>)</span></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p5">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="robbins1.html#K13" title="ROBBINS1:func.13">_1</a> </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"><a href="robbins1.html#K12" title="ROBBINS1:func.12">Double</a> <font color="Maroon" title="c2">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"><span class="p3">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="robbins1.html#K11" title="ROBBINS1:func.11">_0</a> </span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <font color="Maroon" title="c2">x</font></span>)</span></span>)</span>,<font color="Maroon" title="c2">x</font>

<br/>.= 
 <a href="robbins1.html#K10" title="ROBBINS1:func.10">Expand</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> <span class="p0">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="robbins1.html#K15" title="ROBBINS1:func.15">_3</a> </span>)</span></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p5">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="robbins1.html#K13" title="ROBBINS1:func.13">_1</a> </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"><a href="robbins1.html#K12" title="ROBBINS1:func.12">Double</a> <font color="Maroon" title="c2">x</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <font color="Maroon" title="c2">x</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="robbins1.html#K11" title="ROBBINS1:func.11">_0</a> </span>)</span>
<b>by </b><i><a class="txt" href="robbins1.html#E3:87"><i><font color="Green" title="E51">A2</font></i></a>, <a class="ref" href="lattices.html#D5" title="LATTICES:def.5">LATTICES:def 5</a></i>
<br/>.= 
<font color="Maroon" title="c2">x</font> <a href="robbins1.html#K11" title="ROBBINS1:func.11">_0</a> 
<b>by </b><i><a class="ref" href="robbins1.html#T37" target="_self" title="ROBBINS1:th.37">Th37</a></i>
;<br/><br/>


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