(** Addition of functions *)

Lemma Derive_n_iter_plus {I : Type} (l : list I) (f : I -> R -> R) (n: nat) (x : R) :
locally x (fun y => forall (j : I) (k : nat), List.In j l -> (k <= n)%nat -> ex_derive_n (f j) k y) ->
Derive_n (fun y => iter Rplus 0 l (fun j => f j y)) n x =
iter Rplus 0 l (fun j => Derive_n (f j) n x).