Page "Heyting algebra" Paragraph 1

As lattices, Heyting algebras can be shown to be distributive.

Every Boolean algebra is a Heyting algebra when a → b is defined as usual as ¬ a ∨ b, as is every complete distributive lattice when a → b is taken to be the supremum of the set of all c for which a ∧ c ≤ b. The open sets of a topological space form a complete distributive lattice and hence a Heyting algebra.

In the finite case every nonempty distributive lattice, in particular every nonempty finite chain, is automatically bounded and complete and hence a Heyting algebra.