Definition:Bounded Lattice/Definition 2

Definition
Let $\left({S, \vee, \wedge, \preceq}\right)$ be a lattice.

Let $\vee$ and $\wedge$ have identity elements $\bot$ and $\top$ respectively.

Then $\left({S, \vee, \wedge, \preceq}\right)$ is a bounded lattice.

Thus $\left({S, \vee, \wedge}\right)$ is a bounded lattice iff the following axioms are satisfied: