Lemma module_inv_mult_to_inv1 {R : ring} {M : module R} (r : R) (x : M) : @grinv _ (r * x) = ringinv1 r * x. Proof. apply grinv_path_from_op_path. now rewrite <- module_mult_is_rdistr, ringrinvax1, module_mult_0_to_0. Defined.
Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.Algebra.RigsAndRings. Require Import UniMath.Algebra.Groups. Require Import UniMath.Algebra.Monoids.