Definition mate_double_bicat_whiskering : double_bicat_whiskering mate_ver_bicat_sq_bicat_ver_id_comp. Proof. repeat split ; cbn. - refine (λ w x y z h₁ h₂ v₁ v₁' v₂ τ θ, θ • (τ ▹ _)). - exact (λ w x y z h₁ h₂ v₁ v₂ v₂' τ θ, (_ ◃ τ) • θ). - exact (λ w x y z h₁ h₁' h₂ v₁ v₂ τ θ, (pr1 τ ▹ _) • θ). - exact (λ w x y z h₁ h₂ h₂' v₁ v₂ τ θ, θ • (_ ◃ pr1 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.