Definition ps_atan_exists_01 (x : R) (Hx:0 <= x <= 1) :
{l : R | Un_cv (fun N : nat => sum_f_R0 (tg_alt (Ratan_seq x)) N) l}.

Lemma sum_Ratan_seq_opp : forall x n,
sum_f_R0 (tg_alt (Ratan_seq (- x))) n = - sum_f_R0 (tg_alt (Ratan_seq x)) n.