proposition: Lemma cosine_eq_Deriv_sine : forall x, cosine x = Deriv_sine x.
proof: Proof. intro x. assert (T1 := sum_sums _ cos_infinite_cv_radius x) ; assert (T2 := sum_derive_sums _ sin_infinite_cv_radius x). symmetry ; eapply Rpser_unique_extentionality. apply Deriv_sin_seq_simpl. apply T2. apply T1. 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