Definition horizontal_prebicat_2_id_comp_struct : prebicat_2_id_comp_struct horizontal_prebicat_1_id_comp_cells. Proof. repeat split ; cbn. - exact (λ x y f, id_v_square f). - exact (λ x y f, lunitor_h f). - exact (λ x y f, runitor_h f). - exact (λ x y f, linvunitor_h f). - exact (λ x y f, rinvunitor_h f). - exact (λ w x y z f g h, rassociator_h f g h). - exact (λ w x y z f g h, lassociator_h f g h). - exact (λ x y f g h s₁ s₂, transportf_square (id_v_left _) (id_v_left _) (s₁ ⋆v s₂)). - exact (λ x y z f g₁ g₂ s, id_v_square f ⋆h s). - exact (λ x y z f₁ f₂ g s, s ⋆h id_v_square g). Defined.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.Core.Setcategories. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.TwoSidedDispCat. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Isos. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.Core.Strictness. 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.