Definition hor_cyl_twosided_disp_cat_ob_mor : twosided_disp_cat_ob_mor (hom_h w y) (hom_h x z). Proof. simple refine (_ ,, _). - exact (λ (h : w --> y) (k : x --> z), square_double_bicat h k v₁ v₂). - exact (λ (h₁ h₂ : w --> y) (k₁ k₂ : x --> z) (s₁ : square_double_bicat h₁ k₁ v₁ v₂) (s₂ : square_double_bicat h₂ k₂ v₁ v₂) (τ₁ : h₁ ==> h₂) (τ₂ : k₁ ==> k₂), is_hor_cylinder s₁ s₂ τ₁ τ₂). Defined.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.TwoSidedDispCat. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Isos. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Univalence. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Discrete. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.Core.BicategoryLaws. Require Import UniMath.Bicategories.DoubleCategories.DoubleBicat.VerityDoubleBicat. Require Import UniMath.Bicategories.DoubleCategories.DoubleBicat.DerivedLaws.