Meet Absorbs Join

From ProofWiki
Jump to navigation Jump to search


Let $\left({S, \vee, \preceq}\right)$ be a join semilattice.

Let $\wedge$ denote meet.

Then $\wedge$ absorbs $\vee$.

That is, for all $a, b \in S$:

$a \wedge \left({a \vee b}\right) = a$


By Dual Pairs (Order Theory), we observe that the theorem statement is dual to that of Join Absorbs Meet.

The result follows by the Global Duality Principle.



The dual to this theorem is Join Absorbs Meet.