Section Equivalence.
End Equivalence.
Hint Unfold iff: extcore.
(** Backward direction of the equivalences above does not need assumptions *)
(** Some equivalences *)

Theorem or_assoc : forall A B C : Prop, (A \/ B) \/ C <-> A \/ B \/ C.
Lemma iff_and : forall A B : Prop, (A <-> B) -> (A -> B) /\ (B -> A).