Proposition from_comp_enriched_profunctor_ob_comm (y : C₂) {v : V} (fs : ∏ (y : C₂), P y x ⊗ Q z y --> v) (ps : ∏ (y₁ y₂ : C₂), lmap_e P y₂ y₁ x #⊗ identity (Q z y₁) · fs y₁ = sym_mon_braiding V _ _ #⊗ identity (Q z y₁) · mon_lassociator _ _ _ · identity (P y₂ x) #⊗ rmap_e Q z y₁ y₂ · fs y₂) : comp_enriched_profunctor_in y · from_comp_enriched_profunctor_ob fs ps = fs y. Proof. apply (from_enriched_profunctor_coend_comm comp_enriched_profunctor_coend). Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.Limits.Coends. Require Import UniMath.CategoryTheory.OppositeCategory.Core. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. 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.EnrichedCats.Profunctors.Coend. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.Monoidal.Structure.Symmetric. Require Import UniMath.CategoryTheory.Monoidal.Structure.Closed. Import MonoidalNotations.