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_NoDup : forall m (Hm : NoDupA (@eqk elt) m)(f:elt->elt'),
NoDupA (@eqk elt') (map f m).