Proposition associator_profunctor_inv_mor_comm {C₁ C₂ C₃ C₄ : category} (P₁ : C₁ ↛ C₂) (P₂ : C₂ ↛ C₃) (P₃ : C₃ ↛ C₄) (z : C₄) (w : C₁) (y : C₃) (h : P₃ z y) (kl : comp_profunctor_ob P₁ P₂ y w) : associator_profunctor_inv_mor P₁ P₂ P₃ z w (comp_profunctor_ob_in (comp_profunctor P₁ P₂) P₃ y kl h) = associator_profunctor_inv_mor_ob P₁ P₂ P₃ z w y h kl. Proof. unfold associator_profunctor_inv_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.