Proposition lunitor_profunctor_nat_trans_mor_comm {C₁ C₂ : category} (P : profunctor C₁ C₂) {y : C₂} {x x' : C₁} (f : x' --> x) (h : P y x') : lunitor_profunctor_nat_trans_mor P y x (comp_profunctor_ob_in (id_profunctor C₁) P x' f h) = rmap P f h. Proof. unfold lunitor_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.