Fixpoint pow2 (n : nat) : nat :=
  match n with
    | O => 1%nat
    | S n => (2 * pow2 n)%nat
  end.

Lemma sum_f_n_Sm (u : nat -> R) (n m : nat) : (n <= m)%nat -> sum_f n (S m) u = sum_f n m u + u (S m).