(* When a sequence of derivable functions converge pointwise towards a function g, with the derivatives converging uniformly towards a function g', then the function g' is the derivative of g. *)

Lemma CVU_derivable :
forall f f' g g' c d,
CVU f' g' c d ->
(forall x, Boule c d x -> Un_cv (fun n => f n x) (g x)) ->
(forall n x, Boule c d x -> derivable_pt_lim (f n) x (f' n x)) ->
forall x, Boule c d x -> derivable_pt_lim g x (g' x).