Definition horizontal_dual_ver_sq_bicat_id_comp_cells : ver_sq_bicat_id_comp_cells horizontal_dual_ver_sq_bicat_ver_id_comp. Proof. repeat split ; cbn. - exact (λ (x y : B) (v : x -|-> y), id2 v). - exact (λ (x y : B) (v : x -|-> y), lunitor (C := op2_bicat 𝕍) v). - exact (λ (x y : B) (v : x -|-> y), runitor (C := op2_bicat 𝕍) v). - exact (λ (x y : B) (v : x -|-> y), linvunitor (C := op2_bicat 𝕍) v). - exact (λ (x y : B) (v : x -|-> y), rinvunitor (C := op2_bicat 𝕍) v). - exact (λ (w x y z : B) (v₁ : w -|-> x) (v₂ : x -|-> y) (v₃ : y -|-> z), rassociator (C := op2_bicat 𝕍) v₁ v₂ v₃). - exact (λ (w x y z : B) (v₁ : w -|-> x) (v₂ : x -|-> y) (v₃ : y -|-> z), lassociator (C := op2_bicat 𝕍) v₁ v₂ v₃). - exact (λ (x y : B) (v₁ v₂ v₃ : x -|-> y) (τ : v₂ =|=> v₁) (θ : v₃ =|=> v₂), θ • τ). - exact (λ (x y z : B) (v : x -|-> y) (w₁ w₂ : y -|-> z) (τ : w₂ =|=> w₁), v ◃ τ). - exact (λ (x y z : B) (v₁ v₂ : x -|-> y) (w : y -|-> z) (τ : v₂ =|=> v₁), τ ▹ w). 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.