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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_C4 :
forall (An:nat -> R) (k:R),
0 <= k < 1 ->
(forall n:nat, 0 < An n) ->
Un_cv (fun n:nat => Rabs (An (S n) / An n)) k ->
{ l:R | Un_cv (fun N:nat => sum_f_R0 An N) l }.