proposition: Lemma is_derive_mult : forall (f g : R -> R) (x : R) (df dg : R), is_derive f x df -> is_derive g x dg -> is_derive (fun t : R => f t * g t) x (df * g x + f x * dg) .
proof: Proof. intros f g x df dg Df Dg. eapply filterdiff_ext_lin. apply @filterdiff_mult_fct with (2 := Df) (3 := Dg). exact Rmult_comm. rewrite /scal /= /mult /plus /= => y. ring. Qed.
imports: Coq(Reals Psatz ssreflect) Rcomplements Rbar Lim_seq Iter Hierarchy Continuity Equiv