Meet Absorbs Join

Theorem
Let $\struct {S, \vee, \preceq}$ be a join semilattice.

Let $\wedge$ denote meet.

Then $\wedge$ absorbs $\vee$.

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


 * $a \wedge \paren {a \vee b} = a$

Proof
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.

Duality
The dual to this theorem is Join Absorbs Meet.