(************************************************************************)
(*         *      The Rocq Prover / The Rocq Development Team           *)
(*  v      *         Copyright INRIA, CNRS and contributors             *)
(* <O___,, * (see version control and CREDITS file for authors & dates) *)
(*   \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)         *)
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Local Open Scope R_scope.

Lemma MVT_cor3 :
forall (f f':R -> R) (a b:R),
a < b ->
(forall x:R, a <= x -> x <= b -> derivable_pt_lim f x (f' x)) ->
exists c : R, a <= c /\ c <= b /\ f b = f a + f' c * (b - a).