Definition underlying_vert_two_cat_data : two_cat_data. Proof. use make_two_cat_data. - exact underlying_vert_precategory_data. - exact (λ x y v₁ v₂, square v₁ v₂ (identity_h x) (identity_h y)). - exact (λ x y f, id_h_square f). - cbn. refine (λ x y v₁ v₂ v₃ s₁ s₂, _). refine (transportf_square (id_v_right _ @ id_v_left _) (id_v_right _ @ id_v_left _) (linvunitor_h _ ⋆v s₁ ⋆h s₂ ⋆v lunitor_h _)). - exact (λ x y z v w₁ w₂ s, id_h_square v ⋆v s). - exact (λ x y z v₁ v₂ w s, s ⋆v id_h_square w). Defined.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.Core.Setcategories. Require Import UniMath.CategoryTheory.Core.TwoCategories. Require Import UniMath.CategoryTheory.Monads.Monads. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.TwoSidedDispCat. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Isos. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Univalence. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Strictness. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Examples.Comma. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Examples.BicatOfUnivCats. Require Import UniMath.Bicategories.DoubleCategories.Basics.DoubleCategoryBasics. Require Import UniMath.Bicategories.DoubleCategories.Core.DoubleCats. Require Import UniMath.Bicategories.DoubleCategories.Core.UnivalentDoubleCats. Require Import UniMath.Bicategories.DoubleCategories.Core.PseudoDoubleSetCats. Require Import UniMath.Bicategories.DoubleCategories.DerivedLaws. Import TransportSquare.