Proposition profunctor_nat_trans_rmap {C₁ C₂ : category} {P Q : profunctor C₁ C₂} (τ : profunctor_nat_trans P Q) {y : C₂} {x₁ x₂ : C₁} (f : x₁ --> x₂) (h : P y x₁) : τ y x₂ (rmap P f h) = rmap Q f (τ y x₁ h). Proof. rewrite rmap_functor. rewrite (profunctor_nat_trans_natural τ (identity _) f h). 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.