Lemma module_mult_is_rdistr {R : ring} {M : module R} (r s : R) (x : M) : (op1 r s) * x = r * x + s * x. Proof. exact (maponpaths (λ r, pr1setofendabgr r x) (pr1 (pr1 (pr2 (pr2module M))) r s)). Defined.
Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.Algebra.RigsAndRings. Require Import UniMath.Algebra.Groups. Require Import UniMath.Algebra.Monoids.