proposition: Lemma Diffble_I_n_cmul : forall (n : nat) (f : PartFunct IR) (c : IR), Diffble_I_n Hab n f -> Diffble_I_n Hab n (c{**}f).
proof: Proof. intros. assert ({f0' : CSetoid_fun (subset (Compact (less_leEq _ _ _ Hab))) IR | Derivative_I_n Hab n f (PartInt f0')}). apply Diffble_I_n_imp_deriv_n. exact X. inversion_clear X0. apply deriv_n_imp_Diffble_I_n with (c{**}PartInt x). apply Derivative_I_n_cmul. exact X1. 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