Definition:Distributive Lattice/Definition 2

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

Then $\struct {S, \vee, \wedge, \preceq}$ is distributive $\struct {S, \vee, \wedge, \preceq}$ satisfies all of the distributive lattice axioms:

Also see

 * Equivalence of Definitions of Distributive Lattice