Definition tensor_eqi'''_to_eq {C : univalent_category} (TC TD : tensor C) : tensor_eqi''' TC TD -> TC = TD. Proof. intro te. use total2_paths_f. - use total2_paths_f. + exact (tensor_eqi'''_to_eq1 TC TD te). + repeat (apply funextsec ; intro). etrans. 2: apply (pr2 te). etrans. { apply transport_of_bifunctor_map_is_pointwise. } unfold double_transport. unfold tensor_eqi'''_to_eq1. rewrite toforallpaths_funextsec. rewrite toforallpaths_funextsec. rewrite toforallpaths_funextsec. apply independent_transportation_commutes. - use total2_paths_f. + abstract (repeat (apply impred_isaprop ; intro) ; apply homset_property). + abstract (repeat (apply impred_isaprop ; intro) ; apply homset_property). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Functors. Require Import UniMath.CategoryTheory.DisplayedCats.Total. Require Import UniMath.CategoryTheory.DisplayedCats.Constructions. Require Import UniMath.Bicategories.Core.Bicat. Require Import UniMath.Bicategories.Core.Examples.BicatOfUnivCats. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Require Import UniMath.Bicategories.DisplayedBicats.DispUnivalence. Require Import UniMath.Bicategories.DisplayedBicats.DispInvertibles. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.MonoidalCategories.UnivalenceMonCat.CurriedMonoidalCategories. Import TensorNotation. Import TensorNotation.