Definition mate_ver_bicat_sq_bicat_ver_id_comp_sq : ver_bicat_sq_bicat_ver_id_comp_sq mate_ver_bicat_sq_bicat. Proof. split. - exact (λ x y v, runitor _ • linvunitor _). - refine (λ x₁ x₂ x₃ y₁ y₂ y₃ h₁ h₂ h₃ v₁ v₂ w₁ w₂ τ θ, _). exact (lassociator _ _ _ • (τ ▹ _) • rassociator _ _ _ • (_ ◃ θ) • lassociator _ _ _). 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.