proposition: Lemma D_comp : forall n f g, D n f -> D n g -> D n (comp f g).
proof: Proof. intro n ; induction n ; intros f g Dnf Dng ; inversion Dnf ; inversion Dng ; subst. constructor. apply D_S with (derivable_comp _ _ pr0 pr) ; apply D_ext with (fun x => (derive f pr) (g x) * (derive g pr0) x)%R. intro x ; symmetry ; unfold derive ; rewrite Rmult_comm ; apply derive_pt_comp. eapply D_mult. fold (comp (derive f pr) g). apply IHn ; [| apply D_pred] ; assumption. 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