Proposition lmap_e_arr_rmap_e_arr {V : sym_mon_closed_cat} {C₁ C₂ : category} {E₁ : enrichment C₁ V} {E₂ : enrichment C₂ V} (P : E₁ ↛e E₂) {x₁ x₂ : C₁} (f : x₂ --> x₁) {y₁ y₂ : C₂} (g : y₁ --> y₂) : lmap_e_arr P _ g · rmap_e_arr P f _ = rmap_e_arr P f _ · lmap_e_arr P _ g. Proof. unfold lmap_e_arr. rewrite !assoc'. rewrite <- rmap_e_arr_lmap_e. rewrite !assoc. apply maponpaths_2. rewrite !assoc'. rewrite <- tensor_split'. rewrite tensor_split. rewrite !assoc. rewrite tensor_linvunitor. apply idpath. Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.OppositeCategory.Core. Require Import UniMath.CategoryTheory.EnrichedCats.Enrichment. Require Import UniMath.CategoryTheory.EnrichedCats.EnrichmentFunctor. Require Import UniMath.CategoryTheory.EnrichedCats.Enriched.Enriched. Require Import UniMath.CategoryTheory.EnrichedCats.Enriched.EnrichmentEquiv. Require Import UniMath.CategoryTheory.EnrichedCats.Examples.Tensor. Require Import UniMath.CategoryTheory.EnrichedCats.Bifunctors.WhiskeredBifunctors. Require Import UniMath.CategoryTheory.EnrichedCats.Examples.SelfEnriched. Require Import UniMath.CategoryTheory.EnrichedCats.Examples.OppositeEnriched. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors. Require Import UniMath.CategoryTheory.Monoidal.Structure.Symmetric. Require Import UniMath.CategoryTheory.Monoidal.Structure.Closed. Import MonoidalNotations. Section FromEnrichedProfunctor. End FromEnrichedProfunctor.