Definition gregarious_univalent_double_cat_to_verity_double_bicat (C : univalent_double_cat) : gregarious_univalent (double_cat_to_verity_double_bicat C). Proof. use hor_globally_univalent_to_gregarious_univalent. - exact (locally_univalent_double_cat_to_verity_double_bicat C). - exact (hor_globally_univalent_double_cat_to_verity_double_bicat C). - exact (double_cat_vertically_saturated C). Defined.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.TwoSidedDispCat. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Examples.DiscreteBicat. Require Import UniMath.Bicategories.DoubleCategories.DoubleBicat.Core. Require Import UniMath.Bicategories.DoubleCategories.Basics.DoubleCategoryBasics. Require Import UniMath.Bicategories.DoubleCategories.Core.DoubleCats. Require Import UniMath.Bicategories.DoubleCategories.DerivedLaws.TransportLaws. Require Import UniMath.Bicategories.DoubleCategories.Core.UnivalentDoubleCats. Require Import UniMath.Bicategories.DoubleCategories.Core.CompanionsAndConjoints. Require Import UniMath.Bicategories.DoubleCategories.Underlying.HorizontalBicategory.