proposition: Lemma isbinopeqrel_subgr_eqrel {A : abgr} (B : @subabgr A) : isbinophrel (make_eqrel (subgrhrel B) (iseqrel_subgrhrel A B)).
proof: Proof. use isbinophrelif. - apply (pr2 (pr2 A)). - intros a b c X. cbn in *. unfold ishinh_UU in *. use (squash_to_prop X (propproperty _)). intros X''. use hinhpr. use tpair. + exact (pr1 X''). + cbn. set (tmp := pr2 X''). cbn in tmp. rewrite tmp. clear tmp. clear X''. rewrite grinvop. rewrite (commax A c). rewrite (assocax A). rewrite (commax A c). rewrite (assocax A). rewrite grlinvax. rewrite runax. apply idpath. Qed.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.MoreFoundations.PartA UniMath.Algebra.BinaryOperations UniMath.Algebra.Monoids UniMath.Algebra.Groups UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Monics UniMath.CategoryTheory.Epis UniMath.CategoryTheory.PrecategoryBinProduct UniMath.CategoryTheory.CategoriesWithBinOps UniMath.CategoryTheory.PrecategoriesWithAbgrops UniMath.CategoryTheory.opp_precat UniMath.CategoryTheory.Limits.Zero UniMath.CategoryTheory.Limits.Kernels UniMath.CategoryTheory.Limits.Cokernels