Proposition inv_enriched_profunctor_transformation_laws : enriched_profunctor_transformation_laws (pointwise_inv_enriched_profunctor_transformation Hτ). Proof. split. - intros y₁ y₂ x ; cbn. unfold pointwise_inv_enriched_profunctor_transformation. use z_iso_inv_on_left ; cbn. rewrite !assoc'. rewrite <- enriched_profunctor_transformation_lmap_e. rewrite !assoc. rewrite <- tensor_comp_id_l. rewrite z_iso_after_z_iso_inv. rewrite tensor_id_id. rewrite id_left. apply idpath. - intros y x₁ x₂ ; cbn. unfold pointwise_inv_enriched_profunctor_transformation. use z_iso_inv_on_left ; cbn. rewrite !assoc'. rewrite <- enriched_profunctor_transformation_rmap_e. rewrite !assoc. rewrite <- tensor_comp_id_l. rewrite z_iso_after_z_iso_inv. rewrite tensor_id_id. rewrite id_left. 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.EnrichmentTransformation. Require Import UniMath.CategoryTheory.EnrichedCats.Examples.Tensor. Require Import UniMath.CategoryTheory.EnrichedCats.Profunctors.Profunctor. Require Import UniMath.CategoryTheory.EnrichedCats.Profunctors.StandardProfunctors. Require Import UniMath.CategoryTheory.EnrichedCats.Profunctors.ProfunctorTransformations. Require Import UniMath.CategoryTheory.EnrichedCats.Profunctors.ProfunctorSquares. 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.