proposition: Lemma Rpser_abs_cv_radius_weak : forall (An : Rseq) (r : R), Cv_radius_weak An r -> forall x, Rabs x < r -> { l | Rpser_abs An x l}.
proof: Proof. intros An r Rho x x_bd ; assert (Rho' := proj1 (Cv_radius_weak_abs An r) Rho) ; pose (l := weaksum_r (| An |) r Rho' (Rabs x)) ; exists l ; rewrite Rpser_abs_unfold ; apply weaksum_r_sums ; rewrite Rabs_Rabsolu ; assumption. Qed.
imports: Reals Fourier Lra Rpow_facts Rinterval Rextensionality Rsequence_facts Rsequence_sums_facts Rsequence_rewrite_facts RFsequence RFsequence_facts Rpser_def Rpser_def_simpl Rpser_base_facts Rpser_cv_facts Rpser_sums MyINR