Definition transpose_ver_bicat_sq_bicat_ver_id_comp_sq : ver_bicat_sq_bicat_ver_id_comp_sq transpose_ver_bicat_sq_bicat. Proof. split. - exact (λ (x y : B) (v : x -|-> y), id_h_square_bicat v). - exact (λ (x₁ y₁ z₁ x₂ y₂ z₂ : B) (vx : x₁ -|-> x₂) (vy : y₁ -|-> y₂) (vz : z₁ -|-> z₂) (h₁ : x₁ --> y₁) (h₂ : y₁ --> z₁) (k₁ : x₂ --> y₂) (k₂ : y₂ --> z₂) (s₁ : square_double_bicat h₁ k₁ vx vy) (s₂ : square_double_bicat h₂ k₂ vy vz), s₁ ⋆h 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.BicategoryLaws. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.DoubleCategories.DoubleBicat.VerityDoubleBicat. Require Import UniMath.Bicategories.DoubleCategories.DoubleBicat.UnderlyingCats.