proposition: Lemma setwith2binop_equiv_is_z_iso (X Y : ob setwith2binop_category) (f : twobinopiso X Y) : @is_z_isomorphism setwith2binop_precategory X Y (make_twobinopfun (pr1 (pr1 f)) (pr2 f)).
proof: Proof. exists (make_twobinopfun (pr1 (pr1 (invtwobinopiso f))) (pr2 (invtwobinopiso f))). split. - use twobinopfun_paths. use funextfun. intros x. use homotinvweqweq. - use twobinopfun_paths. use funextfun. intros y. use homotweqinvweq. Defined.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.Foundations.UnivalenceAxiom UniMath.Algebra.BinaryOperations UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Univalence