Proposition profunctor_nat_trans_eq_pointwise {C₁ C₂ : category} {P Q : profunctor C₁ C₂} {τ τ' : profunctor_nat_trans P Q} (p : τ = τ') {y : C₂} {x : C₁} (h : P y x) : τ y x h = τ' y x h. Proof. induction p. apply idpath. Qed.
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.