End AbelianGroup1.
(** Sum *)
Section Sums.
Context {G : AbelianGroup}.
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_loc (a b : nat -> G) (n m : nat) :
(forall k, (n <= k <= m)%nat -> a k = b k) ->
sum_n_m a n m = sum_n_m b n m.