End Cutting.
Notation firstn := firstn.
Notation skipn := skipn.
Section CuttingMap.
Variables A B : Type.
Variable f : A -> B.

(* Specifications: *)
Lemma firstn_map : forall n l,
firstn n (map f l) = map f (firstn n l).
Lemma skipn_map : forall n l,
skipn n (map f l) = map f (skipn n l).