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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><b> such that </b><br/><a NAME="E2:24"/><i><font color="Green">E10</font></i>: 
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 <br/>( <font color="Maroon">c<sub>2</sub></font> <a href="robbins1.html#K5" target="_self">+</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> )
 <b>by </b><i><a class="ref" href="robbins1.html#T5" target="_self">Th5</a></i>;<br/>
<a NAME="E3:24"/>
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 <br/>( <font color="Olive">b<sub>1</sub></font> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> )
 
<b>by </b><i><a class="txt" href="robbins1.html#E2:24"><i><font color="Green">E10</font></i></a></i>;<br/>
<b>hence </b><a NAME="E4:24"/>
<font color="Maroon">c<sub>1</sub></font> is <a href="lattices.html#V14">upper-bounded</a>
 <b>by </b><i><a class="txt" href="robbins1.html#E2:24"><i><font color="Green">E10</font></i></a>, <a class="ref" href="lattices.html#D14">LATTICES:def 14</a></i>;<br/>


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