proposition: Lemma Derivative_I_n_inv : forall (n : nat) (f f' : PartFunct IR), Derivative_I_n Hab n f f' -> Derivative_I_n Hab n (Finv f) (Finv f').
proof: Proof. intro. induction n. intros. simpl. simpl in X. apply Feq_inv. exact X. intros. simpl. destruct X. exists (IInv x). apply Derivative_I_wdr with (Finv (PartInt x)). apply part_int_inv. apply Feq_reflexive. apply derivative_imp_inc' with f. exact d. apply Derivative_I_inv. exact d. apply Derivative_I_n_wdl with (Finv (PartInt x)). apply part_int_inv. apply Feq_reflexive. apply derivative_imp_inc' with f. exact d. apply IHn. exact d0. Qed.
imports: ssreflect CSetoids CSetoidFun CFields CPolynomials Program Omega Equivalence Morphisms Wf Morphisms CRings CRing_Homomorphisms Rational Setoid CPoly_NthCoeff CPoly_Degree CReals Intervals CauchySeq IntervalFunct MoreIntervals MoreFunctions Composition seq bigopsClass Structures