Proposition associator_profunctor_nat_trans_mor_comm {C₁ C₂ C₃ C₄ : category} (P₁ : C₁ ↛ C₂) (P₂ : C₂ ↛ C₃) (P₃ : C₃ ↛ C₄) (z : C₄) (w : C₁) (x : C₂) (h : P₁ x w) (kl : comp_profunctor_ob P₂ P₃ z x) : associator_profunctor_nat_trans_mor P₁ P₂ P₃ z w (comp_profunctor_ob_in P₁ (comp_profunctor P₂ P₃) x h kl) = associator_profunctor_nat_trans_mor_ob P₁ P₂ P₃ _ _ x h kl. Proof. unfold associator_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.