Proposition from_enriched_profunctor_coend_comm (v : V) (fs : ∏ (x : C), P x x --> v) (ps : ∏ (x y : C), lmap_e P y x x · fs x = rmap_e P y x y · fs y) (x : C) : enriched_profunctor_coend_in x · from_enriched_profunctor_coend v fs ps = fs x. Proof. unfold enriched_profunctor_coend_in, from_enriched_profunctor_coend. rewrite !assoc'. rewrite CoequalizerCommutes. apply (CoproductInCommutes _ _ _ ob_coprod). 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.