Lemma module_mult_0_to_0 {R : ring} {M : module R} (x : M) : ringunel1 * x = @unel M. Proof. unfold module_mult. cbn. assert (pr2module M ringunel1 = @ringunel1 (ringofendabgr M)). - exact (rigfun_to_unel_rigaddmonoid (pr2module M)). - rewrite X. reflexivity. Defined.
Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.Algebra.RigsAndRings. Require Import UniMath.Algebra.Groups. Require Import UniMath.Algebra.Monoids.