Proposition rwhisker_profunctor_nat_trans_mor_comm {C₁ C₂ C₃ : category} {P₁ P₂ : C₁ ↛ C₂} (τ : profunctor_nat_trans P₁ P₂) (Q : C₂ ↛ C₃) {z : C₃} {y : C₂} {x : C₁} (h : P₁ y x) (h' : Q z y) : rwhisker_profunctor_nat_trans_mor τ Q z x (comp_profunctor_ob_in P₁ Q y h h') = comp_profunctor_ob_in P₂ Q y (τ y x h) h'. Proof. unfold rwhisker_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.