Lemma isarchring_isarchgr {X : ring} (R : hrel X) : R 1%ring 0%ring → istrans R → isbinophrel (X := X) R → isarchring R → isarchgr (X := X) R. Proof. intros Hr0 Hr Hop1 H. apply isarchmonoid_isarchgr. apply (isarchrig_isarchmonoid (X := X)). exact Hr0. exact Hr. exact Hop1. now apply isarchring_isarchrig. 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.