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<b>let </b><font color="Maroon">c<sub>1</sub></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#V6" target="_self">join-idempotent</a>  <a href="robbins1.html#L2" target="_self">ComplLattStr</a> ;<br/>

<b>consider </b><font color="Maroon">c<sub>2</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>
<b>take </b><font color="Maroon">c<sub>3</sub></font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="robbins1.html#K3" target="_self">`</a> ;<br/>

<b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>

<b>thus </b><font color="Maroon">c<sub>3</sub></font> <a href="robbins1.html#K4" target="_self">*'</a> <font color="Maroon">c<sub>4</sub></font> = 
<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">c<sub>2</sub></font> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">c<sub>2</sub></font></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="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span></span>)</span> <a href="robbins1.html#K3" target="_self">`</a> 

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span></span>)</span> <a href="robbins1.html#K3" target="_self">`</a> 
<b>by </b><i><a class="ref" href="robbins1.html#T3" target="_self">Th3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span></span>)</span> <a href="robbins1.html#K3" target="_self">`</a> 
<b>by </b><i><a class="ref" href="robbins1.html#T4" target="_self">Th4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></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">c<sub>4</sub></font> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span></span>)</span></span>)</span> <a href="robbins1.html#K3" target="_self">`</a> 
<b>by </b><i><a class="ref" href="lattices.html#D5">LATTICES:def 5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span></span>)</span> <a href="robbins1.html#K3" target="_self">`</a> 
<b>by </b><i><a class="ref" href="robbins1.html#D7" target="_self">Def7</a></i>
<br/>.= 
<font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="ref" href="robbins1.html#T4" target="_self">Th4</a></i>
;<br/>

<b>thus </b><a NAME="E3:27"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span></span>)</span> <a href="robbins1.html#K3" target="_self">`</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="ref" href="robbins1.html#T4" target="_self">Th4</a></i>;<br/>


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