Definition:Distributive Lattice

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

Then $\left({S, \vee, \wedge, \preceq}\right)$ is distributive iff:


 * $\forall x, y, z \in S: x \wedge \left({y \vee z}\right) = \left({x \wedge y}\right) \vee \left({x \wedge z}\right)$

That is, iff $\wedge$ is distributive over $\vee$.

Also see
Join Distributes over Meet in Distributive Lattice