(************************************************************************)
(*         *   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.

Lemma Alt_CVU : forall (f : nat -> R -> R) g h c r,
(forall x, Boule c r x ->Un_decreasing (fun n => f n x)) ->
(forall x, Boule c r x -> Un_cv (fun n => f n x) 0) ->
(forall x, Boule c r x ->
Un_cv (sum_f_R0 (tg_alt  (fun i => f i x))) (g x)) ->
(forall x n, Boule c r x -> f n x <= h n) ->
(Un_cv h 0) ->
CVU (fun N x => sum_f_R0 (tg_alt (fun i => f i x)) N) g c r.