Definition Reste_E (x y:R) (N:nat) : R :=
  sum_f_R0
  (fun k:nat =>
    sum_f_R0
    (fun l:nat =>
      / INR (fact (S (l + k))) * x ^ S (l + k) *
      (/ INR (fact (N - l)) * y ^ (N - l))) (
        pred (N - k))) (pred N).

(* Specifications: *)
Lemma exp_form : forall (x y:R) (n:nat), (0 < n)%nat -> E1 x n * E1 y n - Reste_E x y n = E1 (x + y) n.