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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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Require Export Rtrigo_fun.
Require Export Rtrigo_def.
Require Export Rtrigo_alt.
Require Export Cos_rel.
Require Export Cos_plus.
Local Open Scope nat_scope.
Local Open Scope R_scope.

(* Specifications: *)
Lemma CVN_R_cos :
forall fn:nat -> R -> R,
fn = (fun (N:nat) (x:R) => (-1) ^ N / INR (fact (2 * N)) * x ^ (2 * N)) ->
CVN_R fn.
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Lemma continuity_cos : continuity cos.
Lemma sin_gt_cos_7_8 : sin (7 / 8) > cos (7 / 8).
Definition PI_2_aux : {z | 7/8 <= z <= 7/4 /\ -cos z = 0}.