Definition horizontal_dual_ver_bicat_sq_bicat_ver_id_comp_sq : ver_bicat_sq_bicat_ver_id_comp_sq horizontal_dual_ver_bicat_sq_bicat. Proof. split. - exact (λ (x y : B) (h : y --> x), id_v_square_bicat h). - exact (λ (x₁ x₂ x₃ y₁ y₂ y₃ : B) (h₁ : y₁ --> x₁) (h₂ : y₂ --> x₂) (h₃ : y₃ --> x₃) (v₁ : x₁ -|-> x₂) (v₂ : x₂ -|-> x₃) (w₁ : y₁ -|-> y₂) (w₂ : y₂ -|-> y₃) (s₁ : square_double_bicat h₁ h₂ w₁ v₁) (s₂ : square_double_bicat h₂ h₃ w₂ v₂), s₁ ⋆v s₂). 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.Invertible_2cells. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.Core.UnivalenceOp. Require Import UniMath.Bicategories.Core.Examples.OpMorBicat. Require Import UniMath.Bicategories.Core.Examples.OpCellBicat. Require Import UniMath.Bicategories.DoubleCategories.DoubleBicat.VerityDoubleBicat. Require Import UniMath.Bicategories.DoubleCategories.DoubleBicat.DerivedLaws. Require Import UniMath.Bicategories.DoubleCategories.DoubleBicat.CellsAndSquares. Require Import UniMath.Bicategories.DoubleCategories.DoubleBicat.UnderlyingCats. Require Import UniMath.Bicategories.DoubleCategories.DoubleBicat.LocalUnivalence.