{R : Ring} (M : RightModule R) (n : nat) (f : forall k, (k < n)%nat -> M) (r : R) : ab_sum n f *R r = ab_sum n (fun k Hk => f k Hk *R r) := lm_sum_dist_l (R:=rng_op R) M n f r.
Require Import WildCat. Require Import Spaces.Nat.Core. Require Import Classes.interfaces.canonical_names. Require Import Algebra.Groups.Kernel Algebra.Groups.Image Algebra.Groups.QuotientGroup. Require Import Algebra.AbGroups.AbelianGroup Algebra.AbGroups.Biproduct. Require Import Rings.Ring.