proposition: Lemma constant_is_cst : forall (r : R), constant r == (fun _ => r).
proof: Proof. intros r x ; assert (Hl := sum_sums _ (constant_infinite_cv_radius r) x) ; assert (Hr := Pser_constant_seq r x) ; apply (Rpser_unique _ _ _ _ Hl Hr). Qed.
imports: MyReals MyINR MyNNR Rsequence_def Rsequence_facts Rsequence_cv_facts Rsequence_sums_facts Rsequence_base_facts Rsequence_rewrite_facts Rsequence_usual_facts Rsequence_subsequence PeanoNat Lra Rpser_def Rpser_def_simpl Rpser_base_facts Rpser_cv_facts Rpser_radius_facts Rpser_sums Rpser_derivative Rpser_derivative_facts Rfunction_def Functions Rextensionality Rpow_facts Rinterval Ranalysis_def Ranalysis_def_simpl Ranalysis_continuity Ranalysis_derivability Ranalysis_monotonicity