Proposition associator_profunctor_inv_mor_ob_comm {C₁ C₂ C₃ C₄ : category} (P₁ : C₁ ↛ C₂) (P₂ : C₂ ↛ C₃) (P₃ : C₃ ↛ C₄) (z : C₄) (w : C₁) (y : C₃) (x : C₂) (h : P₃ z y) (k : P₁ x w) (l : P₂ y x) : associator_profunctor_inv_mor_ob P₁ P₂ P₃ z w y h (comp_profunctor_ob_in P₁ P₂ x k l) = comp_profunctor_ob_in P₁ (comp_profunctor P₂ P₃) x k (comp_profunctor_ob_in P₂ P₃ y l h). Proof. unfold associator_profunctor_inv_mor_ob. 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.