Definition disp_inv_to_eq1 {C D : bicat_of_univ_cats} {F : bicat_of_univ_cats⟦C,D⟧} {TC : bidisp_tensor_disp_bicat C} {TD : bidisp_tensor_disp_bicat D} (ptF ptG : TC -->[F] TD) : disp_invertible_2cell (id2_invertible_2cell F) ptF ptG -> pr1 ptF = pr1 ptG. Proof. intro i. apply funextsec ; intro ; apply funextsec ; intro. set (ix := (pr1 i) x x0). cbn in ix. rewrite id_right in ix. rewrite tensor_id in ix. rewrite id_left in ix. exact ix. 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.