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_Sm (a : nat -> G) (n m : nat) : (n <= S m)%nat -> sum_n_m a n (S m) = plus (sum_n_m a n m) (a (S m)).