(** Definition of ps_atan's derivative *)

Definition Datan_seq := fun (x : R) (n : nat) => x ^ (2*n).

Lemma Datan_CVU_prelim : forall c (r : posreal), Rabs c + r < 1 -> CVU (fun N x => sum_f_R0 (tg_alt (Datan_seq x)) N) (fun y : R => / (1 + y ^ 2)) c r.