Definition square_ver_sq_bicat_id_comp_cells : ver_sq_bicat_id_comp_cells square_ver_sq_bicat_ver_id_comp. Proof. repeat split ; cbn. - exact (λ _ _ f, id2 f). - exact (λ _ _ f, linvunitor f). - exact (λ _ _ f, rinvunitor f). - exact (λ _ _ f, lunitor f). - exact (λ _ _ f, runitor f). - exact (λ _ _ _ _ f g h, lassociator f g h). - exact (λ _ _ _ _ f g h, rassociator f g h). - exact (λ _ _ _ _ _ τ θ, θ • τ). - exact (λ _ _ _ f _ _ τ, f ◃ τ). - exact (λ _ _ _ _ _ g τ, τ ▹ g). 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.Morphisms.Adjunctions. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.Core.EquivToAdjequiv. Require Import UniMath.Bicategories.Core.AdjointUnique. Require Import UniMath.Bicategories.DoubleCategories.DoubleBicat.Core.