Definition disp_map_disp_univalent_2_1 (HD : arrow_subbicat_props D) (HB_2_1 : is_univalent_2_1 B) : disp_univalent_2_1 disp_map_bicat_to_disp_bicat. Proof. intros x y f g p hx hy hf hg. induction p. use weqhomot. - refine (disp_map_inv_2cell_weq_disp_invertible_2cell _ _ _ ∘ refactor_weq _ _ _ ∘ weqtotal2 (make_weq _ (HB_2_1 _ _ _ _)) _ ∘ total2_paths_equiv _ _ _)%weq. exact (weq_on_fam HD _ _). - abstract (intro p ; induction p ; use subtypePath ; [ intro ; apply isaprop_is_disp_invertible_2cell | ] ; cbn ; use subtypePath ; [ intro ; apply cellset_property | ] ; apply idpath). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.StreetFibration. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.Core.BicategoryLaws. Require Import UniMath.Bicategories.Core.AdjointUnique. Require Import UniMath.Bicategories.Core.EquivToAdjequiv. Require Import UniMath.Bicategories.Morphisms.FullyFaithful. Require Import UniMath.Bicategories.Morphisms.InternalStreetFibration. Require Import UniMath.Bicategories.Morphisms.InternalStreetOpFibration. Require Import UniMath.Bicategories.Logic.DisplayMapBicat. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Import DispBicat.Notations. Require Import UniMath.Bicategories.DisplayedBicats.DispUnivalence. Require Import UniMath.Bicategories.DisplayedBicats.Examples.Codomain. Require Import UniMath.Bicategories.Limits.Pullbacks.