(** * Mean value theorem *)

Lemma incr_function_le (f : R -> R) (a b : Rbar) (df : R -> R) :
(forall (x : R), Rbar_le a x -> Rbar_le x b -> is_derive f x (df x))
-> ((forall (x : R), Rbar_le a x -> Rbar_le x b -> df x > 0)
-> (forall (x y : R), Rbar_le a x -> x < y -> Rbar_le y b -> f x < f y)).