(** Definition of ps_atan's derivative *)

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

Lemma ps_atan_continuity_pt_1 : forall eps : R, eps > 0 -> exists alp : R, alp > 0 /\ (forall x, x < 1 -> 0 < x -> Rdist x 1 < alp -> dist R_met (ps_atan x) (Alt_PI/4) < eps).