Section Ring1.
Context {K : Ring}.
Definition mult : K -> K -> K := Ring.mult _ (Ring.class K).
Definition one : K := Ring.one _ (Ring.class K).

Lemma sum_n_m_mult_l :
forall (a : K) (u : nat -> K) (n m : nat),
sum_n_m (fun k => mult a (u k)) n m = mult a (sum_n_m u n m).