Definition is_z_iso_to_is_profunctor_nat_iso : is_profunctor_nat_iso τ. Proof. intros y x. use isweq_iso. - exact (θ y x). - abstract (intros h ; exact (profunctor_nat_trans_eq_pointwise (z_iso_inv_after_z_iso τiso) h)). - abstract (intros h ; exact (profunctor_nat_trans_eq_pointwise (z_iso_after_z_iso_inv τiso) h)). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.opp_precat. Require Import UniMath.CategoryTheory.Categories.HSET.All. Require Import UniMath.CategoryTheory.Categories.HSET.SetCoends. Require Import UniMath.CategoryTheory.Profunctors.Core. Require Import UniMath.CategoryTheory.Profunctors.Examples.