proposition: 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: 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.
imports: UniMath.Foundations.NaturalNumbers UniMath.Algebra.RigsAndRings UniMath.Algebra.Groups UniMath.Algebra.DivisionRig UniMath.Algebra.Domains_and_Fields UniMath.Algebra.ConstructiveStructures UniMath.MoreFoundations.Tactics