proposition: 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: Proof. intros Hr0 Hr Hop1 H. apply isarchrig_isarchring. exact Hop1. apply isarchmonoid_isarchrig. exact Hr0. now apply (isarchgr_isarchmonoid (X := X)). 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