proposition: Lemma ex_derive_n_scal_l (f : R -> R) (n : nat) (a x : R) : ex_derive_n f n x -> ex_derive_n (fun y => a * f y) n x.
proof: Proof. case: n x => /= [ | n] x Hf. by []. apply ex_derive_ext with (fun y => a * Derive_n f n y). move => t ; by rewrite Derive_n_scal_l. now apply ex_derive_scal. Qed.
imports: Coq(Reals Psatz ssreflect) Rcomplements Rbar Lim_seq Iter Hierarchy Continuity Equiv