Lemma teqi'''_to_id_to_teqi''' {C : bicat_of_univ_cats} {TC TD : bidisp_tensor_disp_bicat C} (p : tensor_eqi''' TC TD) : id_tensor_eqi''' TC TD (tensor_eqi'''_to_eq TC TD p) = p. Proof. use total2_paths_f. - apply funextsec ; intro x ; apply funextsec ; intro y. etrans. { apply pr_id_tensor_eqi'''_funextsec. } etrans. { apply distributer_funext. } unfold id_tensor_eqi'''_2. unfold tensor_eqi'''_to_eq1. rewrite toforallpaths_funextsec. rewrite toforallpaths_funextsec. apply idpath. - repeat (apply funextsec ; intro). apply homset_property. Qed.
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.