Definition disp_univalent_2_0_disp_mnd_data (HB : is_univalent_2 B) : disp_univalent_2_0 disp_mnd_data. Proof. use sigma_disp_univalent_2_0_with_props. - exact HB. - apply disp_2cells_isaprop_end_bicat. - use disp_2cells_isaprop_prod. + apply disp_2cells_isaprop_cell_unit_bicat. + apply disp_2cells_isaprop_cell_unit_bicat. - apply disp_univalent_2_1_disp_end. - use is_univalent_2_1_dirprod_bicat. + apply disp_univalent_2_1_disp_add_unit. + apply disp_univalent_2_1_disp_add_mu. - apply disp_locally_groupoid_end_bicat. - use disp_locally_groupoid_prod. + apply disp_locally_groupoid_cell_unit_bicat. + apply disp_locally_groupoid_cell_unit_bicat. - apply disp_univalent_2_0_disp_end. exact (pr2 HB). - use is_univalent_2_0_dirprod_bicat. + use total_is_univalent_2_1. * exact (pr2 HB). * apply disp_univalent_2_1_disp_end. + apply disp_univalent_2_disp_add_unit. exact (pr2 HB). + apply disp_univalent_2_disp_add_mu. exact (pr2 HB). Defined.
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.Univalence. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.BicategoryLaws. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.Morphisms.Adjunctions. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.Core.EquivToAdjequiv. Require Import UniMath.Bicategories.PseudoFunctors.Display.PseudoFunctorBicat. Require Import UniMath.Bicategories.PseudoFunctors.PseudoFunctor. Require Import UniMath.Bicategories.PseudoFunctors.Examples.Projection. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Import DispBicat.Notations. Require Import UniMath.Bicategories.DisplayedBicats.DispAdjunctions. Require Import UniMath.Bicategories.DisplayedBicats.DispUnivalence. Require Import UniMath.Bicategories.DisplayedBicats.Examples.DisplayedCatToBicat. Require Import UniMath.Bicategories.DisplayedBicats.Examples.Prod. Require Import UniMath.Bicategories.DisplayedBicats.Examples.FullSub. Require Import UniMath.Bicategories.DisplayedBicats.Examples.Sigma. Require Import UniMath.Bicategories.DisplayedBicats.Examples.EndoMap.