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<b>let </b><font color="Maroon">L</font> be  non <a href="struct_0.html#V3">empty</a> <a href="lattices.html#V4">join-commutative</a> <a href="lattices.html#V5">join-associative</a> <a href="robbins1.html#V5" target="_self">Huntington</a>  <a href="robbins1.html#L2" target="_self">ComplLattStr</a> ;<br/><b>let </b><font color="Maroon">a</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>, <font color="Maroon">b</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>;<br/>



<b>set </b><font color="Maroon">O</font> = <font color="Maroon">b</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span>;<br/>
<a NAME="E1:34"/><i><font color="Green">E27</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span></span>)</span> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span> <a href="robbins1.html#K3" target="_self">`</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span>
 
<b>by </b><i/>;<br/>
<i><font color="Green">E35</font></i>: <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span></span>)</span> <a href="robbins1.html#K3" target="_self">`</a>  = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">b</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p0">(<span class="default"><font color="Maroon">b</font> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span></span>)</span> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">b</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p0">(<span class="default"><font color="Maroon">b</font> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span></span>)</span> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span></span>)</span> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">b</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p0">(<span class="default"><font color="Maroon">b</font> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span></span>)</span> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">b</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p5">(<span class="default"><font color="Maroon">b</font> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span></span>)</span> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span></span>)</span> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p4">(<span class="default"><font color="Maroon">b</font> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p4">(<span class="default"><font color="Maroon">b</font> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span></span>)</span></span>)</span> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span></span>)</span> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span>
<b>by </b><i><a class="ref" href="robbins1.html#D5" target="_self">Def5</a>, </i>
;<br/>
<font color="Maroon">b</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span></span>)</span> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p4">(<span class="default"><font color="Maroon">b</font> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span></span>)</span> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p4">(<span class="default"><font color="Maroon">b</font> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p4">(<span class="default"><font color="Maroon">b</font> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span></span>)</span></span>)</span> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span>
<b>by </b><i><a class="ref" href="robbins1.html#D6" target="_self">Def6</a>, <a class="ref" href="lattices.html#D5">LATTICES:def 5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p4">(<span class="default"><font color="Maroon">b</font> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p4">(<span class="default"><font color="Maroon">b</font> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span></span>)</span></span>)</span> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span>
<b>by </b><i/>
;<br/>
<b>then </b><i><font color="Green">E36</font></i>: <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span></span>)</span></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p4">(<span class="default"><font color="Maroon">b</font> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p4">(<span class="default"><font color="Maroon">b</font> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span></span>)</span></span>)</span> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span>
<b>by </b><i><a class="ref" href="lattices.html#D5">LATTICES:def 5</a></i>
<br/>.= 
<font color="Maroon">b</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span>
<b>by </b><i/>
;<br/>
<a NAME="E5:34"/><i><font color="Green">E47</font></i>: 
<font color="Maroon">b</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">a</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><font color="Maroon">a</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span></span>)</span> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">a</font> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <span class="p4">(<span class="default"><font color="Maroon">a</font> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span></span>)</span> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">a</font> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">a</font></span>)</span> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">a</font> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">a</font></span>)</span> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">a</font> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">a</font></span>)</span> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="robbins1.html#D6" target="_self">Def6</a>, , </i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span></span>)</span> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">a</font> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">a</font></span>)</span> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">a</font> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">a</font></span>)</span> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="robbins1.html#D6" target="_self">Def6</a>, , <a class="ref" href="robbins1.html#D7" target="_self">Def7</a>, <a class="ref" href="lattices.html#D5">LATTICES:def 5</a></i>
<br/>.= 
<font color="Maroon">a</font>
<b>by </b><i><a class="ref" href="robbins1.html#D6" target="_self">Def6</a>, , <a class="ref" href="robbins1.html#D7" target="_self">Def7</a>, </i>
;<br/><br/>


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