(** *** Proof that tangent is a bijection *)
(* to be removed? *)

Lemma derive_increasing_interv : forall (a b : R) (f : R -> R),
a < b ->
forall (pr:forall x, a < x < b -> derivable_pt f x),
(forall t:R, forall (t_encad : a < t < b), 0 < derive_pt f t (pr t t_encad)) ->
forall x y:R, a < x < b -> a < y < b -> x < y -> f x < f y.