(** * Definitions on [R] *)

Definition Derive (f : R -> R) (x : R) := real (Lim (fun h => (f (x+h) - f x)/h) 0).

Lemma MVT_cor4: forall (f df : R -> R) a eps, (forall c, Rabs (c - a) <= eps -> is_derive f c (df c)) -> forall b, (Rabs (b - a) <= eps) -> exists c, f b - f a = df c * (b - a) /\ (Rabs (c - a) <= Rabs (b - a)).