(************************************************************************)
(*         *      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 Rolle :
forall (f:R -> R) (a b:R) (pr:forall x:R, a < x < b -> derivable_pt f x),
(forall x:R, a <= x <= b -> continuity_pt f x) ->
a < b ->
f a = f b ->
exists c : R, (exists P : a < c < b, derive_pt f c (pr c P) = 0).