Lemma isarchgr_isarchring {X : ring} (R : hrel X) : R 1%ring 0%ring → istrans R → isbinophrel (X := X) R → isarchgr (X := X) R → isarchring R. Proof. intros Hr0 Hr Hop1 H. apply isarchrig_isarchring. exact Hop1. apply isarchmonoid_isarchrig. exact Hr0. now apply (isarchgr_isarchmonoid (X := X)). Defined.
Require Import UniMath.Foundations.NaturalNumbers. Require Import UniMath.Algebra.RigsAndRings. Require Import UniMath.Algebra.Groups. Require Import UniMath.Algebra.DivisionRig. Require Import UniMath.Algebra.Domains_and_Fields. Require Import UniMath.Algebra.ConstructiveStructures. Require Import UniMath.MoreFoundations.Tactics.