Proposition whiskered_enriched_transformation_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_whiskered_bifunctor E₁ E₂ E₃} (τ : whiskered_enriched_transformation F G) : curried_enriched_transformation_law (whiskered_enriched_transformation_to_curried_data τ). Proof. intros x₁ x₂ y₁ y₂ ; cbn. rewrite !assoc'. etrans. { rewrite enriched_comp_postcomp_arr. rewrite !assoc. rewrite <- tensor_comp_mor. rewrite id_right. rewrite whiskered_enriched_transformation_natural_left. apply idpath. } refine (!_). etrans. { rewrite enriched_comp_precomp_arr. rewrite !assoc. rewrite <- tensor_comp_mor. rewrite id_right. rewrite <- whiskered_enriched_transformation_natural_right. apply idpath. } rewrite tensor_comp_r_id_r. rewrite tensor_comp_l_id_r. rewrite !assoc'. apply maponpaths. rewrite precomp_postcomp_arr_assoc. 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.EnrichedCats.Bifunctors.CurriedTransformations. Require Import UniMath.CategoryTheory.EnrichedCats.Bifunctors.WhiskeredBifunctors. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors. Require Import UniMath.CategoryTheory.Monoidal.Structure.Symmetric. Import MonoidalNotations.