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

Lemma mapi_2 : forall (m:t elt)(x:key)(f:key->elt->elt'),
In x (mapi f m) -> In x m.