proposition: Lemma Rseq_norm_abs_Cre : forall (An : nat -> C), {l | Rseq_cv (fun n => sum_f_R0 (fun n =>(Cnorm (An n))) n) l} -> {l | Rseq_cv (fun n => sum_f_R0 (fun n =>(Rabs (Cre (An n))))n) l}.
proof: Proof. intros An H. apply Rseries_CV_comp with (fun n0 : nat => Cnorm (An n0)) . intros n. split. apply Rabs_pos. apply Cre_le_Cnorm. exact H. 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