proposition: Lemma abmonoid_iso_is_equiv (A B : ob abmonoid_category) (f : z_iso A B) : isweq (pr1 (pr1 f)).
proof: Proof. use isweq_iso. - exact (pr1monoidfun _ _ (inv_from_z_iso f)). - intros x. use (toforallpaths _ _ _ (subtypeInjectivity _ _ _ _ (z_iso_inv_after_z_iso f)) x). intros x0. use isapropismonoidfun. - intros x. use (toforallpaths _ _ _ (subtypeInjectivity _ _ _ _ (z_iso_after_z_iso_inv f)) x). intros x0. use isapropismonoidfun. Defined.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.Foundations.UnivalenceAxiom UniMath.Algebra.BinaryOperations UniMath.Algebra.Monoids UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Univalence