Definition:Bounded Lattice/Definition 2

Definition
Let $\struct {S, \vee, \wedge, \preceq}$ be a lattice.

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

Then $\struct {S, \vee, \wedge, \preceq}$ is a bounded lattice.

Thus $\struct {S, \vee, \wedge, \preceq}$ is a bounded lattice the following axioms are satisfied: