Definition:Distributive Lattice

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

Definition 2
That these statements are in fact equivalent is shown on Equivalence of Definitions of Distributive Lattice.

Hence, $\struct {S, \vee, \wedge, \preceq}$ is distributive $\wedge$ and $\vee$ distribute over each other.

Also see

 * Equivalence of Definitions of Distributive Lattice