Lemma module_inv_mult {R : ring} {M : module R} (r : R) (x : M) : @grinv _ (r * x) = r * @grinv _ x. Proof. apply grinv_path_from_op_path. now rewrite <- module_mult_is_ldistr, grrinvax, module_mult_1. Defined.
Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.Algebra.RigsAndRings. Require Import UniMath.Algebra.Groups. Require Import UniMath.Algebra.Monoids.