Definition gregarious_univalent_square_verity_double_bicat (HB_2_0 : is_univalent_2_0 B) (HB_2_1 : is_univalent_2_1 B) : gregarious_univalent square_verity_double_bicat. Proof. use hor_globally_univalent_to_gregarious_univalent. - exact (locally_univalent_square_verity_double_bicat HB_2_1). - exact HB_2_0. - apply square_vertically_saturated. 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.BicategoryLaws. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Morphisms.Adjunctions. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.Core.EquivToAdjequiv. Require Import UniMath.Bicategories.Core.AdjointUnique. Require Import UniMath.Bicategories.DoubleCategories.DoubleBicat.Core.