Definition:Atom of Lattice/Also defined as

Atom of Lattice: Also defined as
Some sources omit the stipulation that an atom of a lattice is not the bottom of that lattice.

By definition of bottom, there exist no $B$ such that $B \prec \bot$.

Hence $B = \bot$ is vacuously true.

Hence:
 * $\forall B \in S: B \prec \bot \implies B = \bot$

is true.

That is, without explicitly stating that an atom is not the bottom, $\bot$ would be classified as an atom vacuously.