Lemma setwith2binop_iso_equiv (X Y : ob setwith2binop_category) : z_iso X Y -> twobinopiso X Y. Proof. intro f. use make_twobinopiso. - exact (make_weq (pr1 (pr1 f)) (setwith2binop_iso_is_equiv X Y f)). - exact (pr2 (pr1 f)). Defined.
Require Import UniMath.Foundations.PartD. Require Import UniMath.Foundations.Propositions. Require Import UniMath.Foundations.Sets. Require Import UniMath.Foundations.UnivalenceAxiom. Require Import UniMath.Algebra.BinaryOperations. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Univalence.