proposition: Lemma binop_iso_is_equiv (A B : ob BINOP) (f : z_iso A B) : isweq (pr1 (pr1 f)).
proof: Proof. apply (isweq_iso _ (pr1binopfun _ _ (inv_from_z_iso f))). - intro x. set (T:=z_iso_inv_after_z_iso f). apply subtypeInjectivity in T. set (T':=toforallpaths _ _ _ T). apply T'. intro x0. apply isapropisbinopfun. - intros y. set (T:=z_iso_after_z_iso_inv f). apply subtypeInjectivity in T. set (T':=toforallpaths _ _ _ T). apply T'. intros x0. apply isapropisbinopfun. 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 UniMath.CategoryTheory.Core.Functors