proposition: Lemma continuity_pt_sum_r : forall (An:nat->R) (r:R) (Pr : finite_cv_radius An r) x, Rabs x < r -> continuity_pt (sum_r An r Pr) x.
proof: Proof. intros An r rho x x_bd ; apply derivable_continuous_pt ; apply derivable_pt_sum_r ; assumption. Qed.
imports: Reals Rpow_facts Rfunction_def Rinterval Rextensionality Ranalysis_def Ranalysis_def_simpl Ranalysis_facts Ranalysis_continuity Ranalysis_derivability Ranalysis_monotonicity Lra MyRIneq Rsequence_facts Rsequence_sums_facts RFsequence RFsequence_facts Rpser_def Rpser_base_facts Rpser_radius_facts Rpser_sums Rpser_sums_facts Tactics