Section ModuleSpace1.
Context {K : Ring} {V : ModuleSpace K}.
Definition scal : K -> V -> V := ModuleSpace.scal _ _ (ModuleSpace.class K V).

Lemma sum_n_m_scal_l :
forall (a : K) (u : nat -> V) (n m : nat),
sum_n_m (fun k => scal a (u k)) n m = scal a (sum_n_m u n m).