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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#V7" target="_self">meet-associative</a> <a href="lattices.html#V8" target="_self">meet-absorbing</a> <a href="lattices.html#V9" target="_self">join-absorbing</a>  <a href="lattices.html#L3" target="_self">LattStr</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font>, <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>assume </b><a NAME="E1:54"/>
<font color="Maroon">c<sub>2</sub></font> <a href="lattices.html#R1" target="_self">[=</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<b>hence </b><span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="lattices.html#K2" target="_self">"/\"</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="lattices.html#K1" target="_self">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="lattices.html#K2" target="_self">"/\"</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="lattices.html#K2" target="_self">"/\"</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="lattices.html#K2" target="_self">"/\"</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="lattices.html#K1" target="_self">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="lattices.html#K2" target="_self">"/\"</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="lattices.html#T21" target="_self">Th21</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="lattices.html#K2" target="_self">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="lattices.html#K2" target="_self">"/\"</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="lattices.html#K1" target="_self">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="lattices.html#K2" target="_self">"/\"</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="lattices.html#D7" target="_self">Def7</a></i>
<br/>.= 
<font color="Maroon">c<sub>3</sub></font> <a href="lattices.html#K2" target="_self">"/\"</a> <font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="ref" href="lattices.html#D8" target="_self">Def8</a></i>
;<br/> <i><font color="Red">:: according to </font></i><a class="ref" href="lattices.html#D3" target="_self">LATTICES:def 3</a><br/>


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