proposition: Lemma derivable_pt_sum_r : forall An r (Pr : finite_cv_radius An r) x, Rabs x < r -> derivable_pt (sum_r An r Pr) x.
proof: Proof. intros An r rho x x_bd ; assert (r_pos: 0 <= r) by (transitivity (Rabs x) ; [apply Rabs_pos | left ; assumption]) ; eapply derivable_Rball_derivable_pt ; [eapply derivable_Rball_sum_r | eapply Rball_0_simpl ; eassumption]. 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