Definition mult_to_ringofendabgr {R : ring} {G : abgr} {m : R -> G -> G} (ax1 : mult_isldistr_wrt_grop m) (r : R) : ringofendabgr G. Proof. use monoidfunconstr. intro x. exact (m r x). apply make_dirprod. + intros x y. apply ax1. + apply (grlcan G (m r (unel G))). rewrite runax. rewrite <- (ax1 r (unel G) (unel G)). rewrite runax. apply idpath. Defined.
Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.Algebra.RigsAndRings. Require Import UniMath.Algebra.Groups. Require Import UniMath.Algebra.Monoids.