0 *L m = 0. Proof. apply (grp_cancelL1 (z := lact 0 m)). lhs_V nrapply lm_dist_r. f_ap. apply rng_plus_zero_r. Defined.
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.