proposition: Lemma bidisp_ru_disp_prebicat_is_globally_univalent : disp_univalent_2_0 bidisp_ru_disp_bicat.
proof: Proof. apply disp_cell_unit_bicat_univalent_2_0. - apply bidisp_tensorunit_is_univalent_2. - intro ; intros. apply isaprop_preserves_runitor. - intro ; apply isaset_runitor. - intros C ru1 ru2 pru. use total2_paths_f. + apply funextsec ; intro. refine (_ @ (pr1 pru x)). refine (! id_left _ @ _). apply cancel_postcomposition. refine (_ @ ! id_right _). apply (! tensor_id _ _ _). + apply isaprop_runitor_nat. Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All 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.CategoryTheory.DisplayedCats.Constructions UniMath.Bicategories.Core.Bicat UniMath.Bicategories.Core.Examples.BicatOfUnivCats UniMath.Bicategories.DisplayedBicats.DispBicat UniMath.Bicategories.DisplayedBicats.DispUnivalence UniMath.Bicategories.DisplayedBicats.Examples.Prod UniMath.Bicategories.DisplayedBicats.Examples.Sigma UniMath.Bicategories.DisplayedBicats.Examples.DisplayedCatToBicat UniMath.Bicategories.Core.Univalence UniMath.Bicategories.MonoidalCategories.UnivalenceMonCat.CurriedMonoidalCategories UniMath.Bicategories.MonoidalCategories.UnivalenceMonCat.TensorLayer UniMath.Bicategories.MonoidalCategories.UnivalenceMonCat.UnitLayer UniMath.Bicategories.MonoidalCategories.UnivalenceMonCat.TensorUnitLayer