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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.
Local Ltac Tauto.intuition_solver ::= auto with rorders real arith.
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(** * Preliminaries                                      *)
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(** ** Various generic lemmas which probably should go somewhere else *)

(* The following two lemmas are general purposes about alternated series. They do not belong here. *)
Lemma Alt_first_term_bound : forall f l N n,
Un_decreasing f -> Un_cv f 0 ->
Un_cv (sum_f_R0 (tg_alt f)) l ->
(N <= n)%nat ->
Rdist (sum_f_R0 (tg_alt f) n) l <= f N.