proposition: Lemma C_opp: forall n f, C n f -> C n (- f)%F.
proof: Proof. intro n ; induction n ; intros f Cnf. inversion_clear Cnf ; constructor ; reg. inversion_clear Cnf ; pose (pr2 := derivable_opp _ pr) ; apply C_S with pr2 ; apply C_ext with (- derive f pr)%F. intro x ; symmetry ; unfold derive ; rewrite derive_pt_eq ; apply derivable_pt_lim_opp; destruct (pr x) as [? Hd]; apply Hd. apply IHn ; assumption. Qed.
imports: Rbase Ranalysis Lia Lra Rfunctions Rfunction_facts Rextensionality Rinterval Ranalysis_def Ranalysis_def_simpl Ranalysis_facts Ranalysis_continuity Ranalysis_derivability Ranalysis_monotonicity Rfunction_classes_def MyR_dist Reals.Tactics