Proposition enriched_profunctor_coend_comm_arr {y₁ y₂ : C} (g : y₁ --> y₂) : lmap_e_arr P y₁ g · enriched_profunctor_coend_in y₁ = rmap_e_arr P g y₂ · enriched_profunctor_coend_in y₂. Proof. unfold lmap_e_arr, rmap_e_arr. rewrite !assoc'. rewrite enriched_profunctor_coend_comm. apply idpath. Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.Limits.Coproducts. Require Import UniMath.CategoryTheory.Limits.Coequalizers. Require Import UniMath.CategoryTheory.EnrichedCats.BenabouCosmos. Require Import UniMath.CategoryTheory.EnrichedCats.Enrichment. Require Import UniMath.CategoryTheory.EnrichedCats.EnrichmentFunctor. Require Import UniMath.CategoryTheory.EnrichedCats.Profunctors.Profunctor. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.Monoidal.Structure.Symmetric. Require Import UniMath.CategoryTheory.Monoidal.Structure.Closed. Import MonoidalNotations.