proposition: Lemma Cpser_derive_finite_sum : forall An n x, derivable_pt_lim (fun x => sum_f_C0 (gt_pser An x) n) x (Cpser_partial_sum_derive An n x).
proof: Proof. intros An n x ; unfold Cpser_partial_sum_derive, gt_pser, An_deriv ; apply (derivable_pt_lim_partial_sum An x n). Qed.
imports: Rinterval Ranalysis_def Rpser_def Rpser_base_facts Rpser_cv_facts Rpser_sums Rpow_facts Rsequence_def Rsequence_facts Rseries_def Rseries_facts RFsequence_facts Cpow Cpser_def Cpser_base_facts CFsequence CFsequence_facts Csequence Csequence_def Csequence_facts Cmet Cnorm Ctacfield Cprop_base Canalysis_def Canalysis_cont Canalysis_deriv Canalysis_basic_facts