{R : Ring} (M : RightModule R) (n : nat) (f : forall k, (k < n)%nat -> R) (x : M) : x *R ab_sum n f = ab_sum n (fun k Hk => x *R f k Hk) := lm_sum_dist_r (R:=rng_op R) M n f x.
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.