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_ext_loc : forall (a b : nat -> G) N, (forall n, (n <= N)%nat -> a n = b n) -> sum_n a N = sum_n b N.