Proposition enriched_nat_trans_to_curried_law {V : sym_monoidal_cat} {C₁ C₂ C₃ : category} {E₁ : enrichment C₁ V} {E₂ : enrichment C₂ V} {E₃ : enrichment C₃ V} {F G : enriched_curried_bifunctor E₁ E₂ E₃} (τ : enriched_nat_trans (enriched_curried_bifunctor_to_bifunctor F) (enriched_curried_bifunctor_to_bifunctor G)) : curried_enriched_transformation_law (enriched_nat_trans_to_curried_data τ). Proof. intros x₁ x₂ y₁ y₂. refine (_ @ pr2 τ (x₁ ,, y₁) (x₂ ,, y₂) @ _) ; cbn. - unfold postcomp_arr, postcompose_underlying_morphism ; cbn. rewrite enriched_from_to_arr. apply idpath. - unfold precomp_arr, precompose_underlying_morphism ; cbn. rewrite enriched_from_to_arr. apply idpath. Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.EnrichedCats.Enrichment. Require Import UniMath.CategoryTheory.EnrichedCats.EnrichmentFunctor. Require Import UniMath.CategoryTheory.EnrichedCats.EnrichmentTransformation. 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.CurriedBifunctors. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors. Require Import UniMath.CategoryTheory.Monoidal.Structure.Symmetric. Import MonoidalNotations.