Definition precatbinprod_z_iso_inv {C D : category} {X X' : C} {Z Z' : D} (α : z_iso X X') (β : z_iso Z Z') : precatbinprod_z_iso (z_iso_inv_from_z_iso α) (z_iso_inv_from_z_iso β) = z_iso_inv_from_z_iso (precatbinprod_z_iso α β). Proof. apply inv_z_iso_unique. split; apply z_iso_inv_after_z_iso. Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.opp_precat.