Lemma module_mult_inv_to_inv1 {R : ring} {M : module R} (r : R) (x : M) : r * @grinv _ x = ringinv1 r * x. Proof. now rewrite <- module_inv_mult_to_inv1, module_inv_mult. Defined.
Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.Algebra.RigsAndRings. Require Import UniMath.Algebra.Groups. Require Import UniMath.Algebra.Monoids.