proposition: Lemma bidisp_unit_disp_prebicat_is_locally_univalent : disp_univalent_2_1 bidisp_unit_disp_bicat.
proof: 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.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Functors UniMath.CategoryTheory.DisplayedCats.Total UniMath.Bicategories.Core.Bicat UniMath.Bicategories.Core.Examples.BicatOfUnivCats UniMath.Bicategories.DisplayedBicats.DispBicat UniMath.Bicategories.DisplayedBicats.DispUnivalence UniMath.Bicategories.MonoidalCategories.UnivalenceMonCat.CurriedMonoidalCategories