proposition: Proposition disp_univalent_2_0_disp_bicat_of_univ_disp_cat : disp_univalent_2_0 disp_bicat_of_univ_disp_cats.
proof: Proof. use fiberwise_univalent_2_0_to_disp_univalent_2_0. intros C D₁ D₂. use weqhomot. - refine (disp_bicat_of_univ_disp_cats_adjequiv_weq D₁ D₂ ∘ univ_disp_cat_eq (pr1 D₁) (pr1 D₂) (pr2 D₁) (pr2 D₂) ∘ path_sigma_hprop _ _ _ _)%weq. apply isaprop_is_univalent_disp. - abstract (intro p ; cbn in p ; induction p ; use subtypePath ; [ intro ; use (isaprop_disp_left_adjoint_equivalence _ _ univalent_cat_is_univalent_2_1 disp_univalent_2_1_disp_bicat_of_univ_disp_cat) | ] ; apply idpath). Defined.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.DisplayedCats.Fibrations UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Functors UniMath.CategoryTheory.DisplayedCats.NaturalTransformations UniMath.CategoryTheory.DisplayedCats.Fibrations UniMath.CategoryTheory.DisplayedCats.Isos UniMath.CategoryTheory.DisplayedCats.Univalence UniMath.CategoryTheory.DisplayedCats.Constructions UniMath.CategoryTheory.DisplayedCats.Adjunctions UniMath.CategoryTheory.DisplayedCats.Equivalences UniMath.CategoryTheory.DisplayedCats.DisplayedFunctorEq UniMath.CategoryTheory.DisplayedCats.EquivalenceOverId UniMath.CategoryTheory.DisplayedCats.DisplayedCatEq UniMath.Bicategories.Core.Bicat UniMath.Bicategories.Core.Invertible_2cells UniMath.Bicategories.Core.EquivToAdjequiv UniMath.Bicategories.Morphisms.Adjunctions UniMath.Bicategories.DisplayedBicats.DispBicat UniMath.Bicategories.DisplayedBicats.DispAdjunctions UniMath.Bicategories.DisplayedBicats.DispInvertibles UniMath.Bicategories.DisplayedBicats.DispUnivalence UniMath.Bicategories.Core.Examples.BicatOfUnivCats UniMath.Bicategories.DisplayedBicats.Examples.FullSub UniMath.Bicategories.DisplayedBicats.Examples.Sigma UniMath.Bicategories.DisplayedBicats.Examples.DisplayedCatToBicat