(** * Conversions between maps and association lists. *)

  Definition uncurry {U V W : Type} (f : U -> V -> W) : U*V -> W :=
   fun p => f (fst p) (snd p).Definition of_list :=
    List.fold_right (uncurry (@add _)) (empty elt).Definition to_list := elements.

Lemma map_induction : forall P : t elt -> Type, (forall m, Empty m -> P m) -> (forall m m', P m -> forall x e, ~In x m -> Add x e m m' -> P m') -> forall m, P m.