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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="robbins1.html#L2" target="_self">ComplLattStr</a> ;<br/>

<b>assume </b><a NAME="E1:36_1_1"/>
( <font color="Maroon">c<sub>1</sub></font> is <a href="lattices.html#V4">join-commutative</a> &amp; <font color="Maroon">c<sub>1</sub></font> is <a href="lattices.html#V5">join-associative</a> &amp; <font color="Maroon">c<sub>1</sub></font> is <a href="robbins1.html#V5" target="_self">Huntington</a> )
 ;<br/>

<a NAME="E2:36_1_1"/><b>then </b>
for <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font> holds <font color="Olive">b<sub>1</sub></font> <a href="robbins1.html#NK4" target="_self">+</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="robbins1.html#T13" target="_self">Th13</a></i>;<br/>
<b>hence </b><a NAME="E3:36_1_1"/>
<font color="Maroon">c<sub>1</sub></font> is <a href="robbins1.html#V6" target="_self">join-idempotent</a>
 <b>by </b><i><a class="ref" href="robbins1.html#D7" target="_self">Def7</a></i>;<br/>


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