proposition: Lemma nth_derive_Rball_ext_weak: forall c r n f g (pr1 : D_Rball c r n f) (pr2 : D_Rball c r n g), f == g -> nth_derive_Rball c r f pr1 == nth_derive_Rball c r g pr2.
proof: Proof. intros c r n ; induction n ; intros f g pr1 pr2 Heq. apply Heq. apply IHn, derive_Rball_ext_strong, Req_Rball_eq ; assumption. Qed.
imports: Reals Rfunction_classes Ranalysis_def Ranalysis_def_simpl Rfunction_def Rextensionality Ranalysis_continuity Ranalysis_derivability Ranalysis_monotonicity Rinterval Nth_derivative_def