Proposition enriched_whiskered_weq_curried_bifunctor_left (F : enriched_whiskered_bifunctor E₁ E₂ E₃) : enriched_curried_bifunctor_whiskered (enriched_whiskered_bifunctor_to_curried F) = F. Proof. use subtypePath. { intro. apply isaprop_enriched_whiskered_bifunctor_laws. } refine (maponpaths (λ z, pr11 F ,, z) _). use pathsdirprod ; cbn. - use funextsec ; intro x₁. use funextsec ; intro x₂. use funextsec ; intro y. etrans. { rewrite !assoc. apply maponpaths_2. rewrite !assoc'. apply maponpaths. rewrite <- tensor_comp_mor. rewrite enriched_whiskered_bifunctor_right_id. rewrite id_left. apply idpath. } rewrite tensor_split'. rewrite !assoc'. rewrite <- enrichment_id_right. rewrite tensor_runitor. rewrite !assoc. rewrite mon_rinvunitor_runitor. apply id_left. - use funextsec ; intro x. use funextsec ; intro y₁. use funextsec ; intro y₂. etrans. { rewrite !assoc. apply maponpaths_2. rewrite !assoc'. apply maponpaths. rewrite <- tensor_comp_mor. rewrite enriched_whiskered_bifunctor_left_id. rewrite id_left. apply idpath. } rewrite tensor_split. rewrite !assoc'. rewrite <- enrichment_id_left. rewrite tensor_lunitor. rewrite !assoc. rewrite mon_linvunitor_lunitor. apply id_left. 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.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. Require Import UniMath.CategoryTheory.Monoidal.Structure.SymmetricDiagonal. Import MonoidalNotations. Section FromWhiskeredBifunctor. End FromWhiskeredBifunctor.