Proposition runitor_profunctor_nat_trans_mor_comm {C₁ C₂ : category} (P : profunctor C₁ C₂) {x : C₁} {y y' : C₂} (g : y --> y') (h : P y' x) : runitor_profunctor_nat_trans_mor P y x (comp_profunctor_ob_in P (id_profunctor C₂) y' h g) = lmap P g h. Proof. unfold runitor_profunctor_nat_trans_mor. rewrite from_comp_profunctor_ob_comm. 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.