proposition: Lemma ex_derive_n_iter_plus {I : Type} (l : list I) (f : I -> R -> R) (n: nat) (x : R) : locally x (fun y => forall (j : I) (k : nat), List.In j l -> (k <= n)%nat -> ex_derive_n (f j) k y) -> ex_derive_n (fun y => iter Rplus 0 l (fun j => f j y)) n x.
proof: Proof. case: n => //= n H. eexists. by apply (is_derive_n_iter_plus l f (S n)). Qed.
imports: Coq(Reals Psatz ssreflect) Rcomplements Rbar Lim_seq Iter Hierarchy Continuity Equiv