proposition: Lemma weaksum_r_sums : forall (An : nat -> R) (r : R) (Pr : Cv_radius_weak An r) (x : R), Rabs x < r -> Rpser An x (weaksum_r An r Pr x).
proof: Proof. intros An r Pr x x_bd. unfold weaksum_r ; case (Rlt_le_dec (Rabs x) r) ; intro s. destruct (Rpser_abel An r Pr x s) as (l,Hl) ; simpl ; assumption. apply False_ind ; lra. Qed.
imports: Reals Rinterval Lra Rpser_def Rpser_base_facts Rpser_cv_facts