(** From the induction principle on [fold], we can deduce some general induction principles on maps. *)

Lemma map_induction_bis :
forall P : t elt -> Type,
(forall m m', Equal m m' -> P m -> P m') ->
P (empty _) ->
(forall x e m, ~In x m -> P m -> P (add x e m)) ->
forall m, P m.