(************************************************************************)
(*         *   The Coq Proof Assistant / The Coq Development Team       *)
(*  v      *   INRIA, CNRS and contributors - Copyright 1999-2018       *)
(* <O___,, *       (see CREDITS file for the list of authors)           *)
(*   \VV/  **************************************************************)
(*    //   *    This file is distributed under the terms of the         *)
(*         *     GNU Lesser General Public License Version 2.1          *)
(*         *     (see LICENSE file for the text of the license)         *)
(************************************************************************)
Local Open Scope R_scope.
(** Tools *)
Definition pos_half_prf : 0 < /2.
(* The following lemmas are general purpose lemmas about squares. They do not belong here *)
(** * Properties of tangent *)
(** 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.