(************************************************************************)
(*         *      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)         *)
(************************************************************************)
Local Open Scope R_scope.

Lemma tech6 :
forall (An:nat -> R) (k:R) (N:nat),
0 <= k ->
(forall i:nat, An (S i) < k * An i) ->
sum_f_R0 An N <= An 0%nat * sum_f_R0 (fun i:nat => k ^ i) N.