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(*         *   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)         *)
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Local Open Scope R_scope.

(* A variant of MVT using absolute values. *)
Lemma MVT_abs :
forall (f f' : R -> R) (a b : R),
(forall c : R, Rmin a b <= c <= Rmax a b ->
derivable_pt_lim f c (f' c)) ->
exists c : R, Rabs (f b - f a) = Rabs (f' c) * Rabs (b - a) /\
Rmin a b <= c <= Rmax a b.