Proposition make_profunctor_nat_trans_law : is_nat_trans _ _ make_profunctor_nat_trans_data. Proof. intros xy₁ xy₂ fg. induction xy₁ as [ y₁ x₁ ]. induction xy₂ as [ y₂ x₂ ]. induction fg as [ g f ]. use funextsec. intro h. pose (H _ _ _ _ g f h) as p. cbn in *. refine (_ @ p @ _) ; clear p. - rewrite lmap_rmap_functor. apply idpath. - rewrite lmap_rmap_functor. 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.