Lemma bidisp_unit_disp_prebicat_is_locally_univalent : disp_univalent_2_1 bidisp_unit_disp_bicat. Proof. apply fiberwise_local_univalent_is_univalent_2_1. intros C D F IC ID puF puG. apply isweqimplimpl. - cbn. intros α. pose (pr1 α) as d. cbn in *. unfold bidisp_unit_disp_2cell_struct in *. unfold preservesunit_commutes in d. rewrite id_right in d. exact d. - apply univalent_category_has_homsets. - apply invproofirrelevance. intro ; intro. use subtypePath. + intro x0. apply isaprop_is_disp_invertible_2cell. + apply univalent_category_has_homsets. 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.Bicategories.Core.Bicat. Require Import UniMath.Bicategories.Core.Examples.BicatOfUnivCats. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Require Import UniMath.Bicategories.DisplayedBicats.DispUnivalence. Require Import UniMath.Bicategories.MonoidalCategories.UnivalenceMonCat.CurriedMonoidalCategories.