Definition mate_ver_sq_bicat_id_comp_cells : ver_sq_bicat_id_comp_cells mate_ver_sq_bicat_ver_id_comp. Proof. repeat split ; cbn. - exact (λ _ _ f, id2 _). - exact (λ _ _ f, linvunitor _). - exact (λ _ _ f, rinvunitor _). - exact (λ _ _ f, lunitor _). - exact (λ _ _ f, runitor _). - exact (λ _ _ _ _ f g h, lassociator _ _ _). - exact (λ _ _ _ _ f g h, rassociator _ _ _). - exact (λ _ _ _ _ _ τ θ, θ • τ). - exact (λ _ _ _ f _ _ τ, _ ◃ τ). - exact (λ _ _ _ _ _ g τ, τ ▹ _). 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.Morphisms.Properties.Composition. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.Core.EquivToAdjequiv. Require Import UniMath.Bicategories.Core.AdjointUnique. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Require Import UniMath.Bicategories.DisplayedBicats.DispUnivalence. Require Import UniMath.Bicategories.DisplayedBicats.Examples.Sub1Cell. Require Import UniMath.Bicategories.DoubleCategories.DoubleBicat.Core.