Definition:Distributive Lattice

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

Then $\left({S, \vee, \wedge, \preceq}\right)$ is distributive iff one (hence all) of the following equivalent statements holds:

That is, $\left({S, \vee, \wedge, \preceq}\right)$ is distributive iff $\wedge$ and $\vee$ distribute over each other.

Equivalence of Definitions
That the conditions above are equivalent is shown on Equivalence of Distributive Lattice Definitions.