Definition:Distributive Lattice

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

Then $\left({L, \preceq}\right)$ is distributive iff:
 * $\forall x, y, z \in L: x \wedge \left({y \vee z}\right) = \left({x \wedge y}\right) \vee \left({x \wedge z}\right)$

where $\wedge$ and $\vee$ denote meet and join respectively.

That is, iff $\wedge$ is distributive over $\vee$ when considered as binary operations in $L$.