(** Addition of functions *)

Lemma Derive_n_plus (f g : R -> R) (n : nat) (x : R) :
locally x (fun y => forall k, (k <= n)%nat -> ex_derive_n f k y) ->
locally x (fun y => forall k, (k <= n)%nat -> ex_derive_n g k y) ->
Derive_n (fun x => f x + g x) n x = Derive_n f n x + Derive_n g n x.