Definition aintdomazerosubmonoid ( A : aintdom ) : @subabmonoid ( ringmultabmonoid A ). Proof. intros. split with ( fun x : A => x # 0 ). split. - intros a b. simpl in *. apply (pr2 (pr2 A)). + simpl in a. apply (pr2 a). + apply (pr2 b). - apply (pr2 A). Defined.
Require Import UniMath.Foundations.PartA. Require Import UniMath.Foundations.Propositions. Require Import UniMath.Foundations.NaturalNumbers. Require Import UniMath.Algebra.RigsAndRings. Require Import UniMath.Algebra.Domains_and_Fields. Require Import UniMath.NumberSystems.Integers. Require Import UniMath.Algebra.Monoids.