(************************************************************************)
(*         *   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 nat_scope.
Local Open Scope R_scope.
Definition Majxy (x y:R) (n:nat) : R :=
Rmax 1 (Rmax (Rabs x) (Rabs y)) ^ (4 * S n) / INR (fact n).

Lemma reste1_maj :
forall (x y:R) (N:nat),
(0 < N)%nat -> Rabs (Reste1 x y N) <= Majxy x y (pred N).