Definition sum_n_m (a : nat -> G) n m :=
  iter_nat plus zero a n m.Definition sum_n (a : nat -> G) n :=
  sum_n_m a O n.

Lemma sum_n_m_ext (a b : nat -> G) n m : (forall n, a n = b n) -> sum_n_m a n m = sum_n_m b n m.