Section Elt2.
(* A new section is necessary for previous definitions to work with different [elt], especially [MapsTo]... *)
Variable elt elt' : Type.
(** Specification of [map] *)

Lemma map_1 : forall (m:t elt)(x:key)(e:elt)(f:elt->elt'),
MapsTo x e m -> MapsTo x (f e) (map f m).