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(*         *      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.
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(* Various versions of the criterion of D'Alembert *)
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Lemma Alembert_C2_aux_Un_cv :
forall Xn : nat -> R,
let Yn i := (2 * Rabs (Xn i) + Xn i) / 2 in
(forall n, Xn n <> 0) ->
Un_cv (fun n:nat => Rabs (Xn (S n) / Xn n)) 0 ->
Un_cv (fun n => Rabs (Yn (S n) / Yn n)) 0.