Proposition lwhisker_profunctor_nat_trans_mor_comm {C₁ C₂ C₃ : category} (P : C₁ ↛ C₂) {Q₁ Q₂ : C₂ ↛ C₃} (τ : profunctor_nat_trans Q₁ Q₂) {z : C₃} {y : C₂} {x : C₁} (h : P y x) (h' : Q₁ z y) : lwhisker_profunctor_nat_trans_mor P τ z x (comp_profunctor_ob_in P Q₁ y h h') = comp_profunctor_ob_in P Q₂ y h (τ z y h'). Proof. unfold lwhisker_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.