Proposition comp_enriched_profunctor_rmap_comm (y : C₂) : (comp_enriched_profunctor_in z x₁ y · comp_enriched_profunctor_rmap) #⊗ identity _ · internal_eval _ _ = sym_mon_braiding _ _ _ · comp_enriched_profunctor_rmap_mor y. Proof. unfold comp_enriched_profunctor_rmap, internal_transpose. rewrite from_comp_enriched_profunctor_ob_comm. rewrite internal_beta. apply idpath. 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.