Definition transpose_double_bicat_whiskering : double_bicat_whiskering transpose_ver_bicat_sq_bicat_ver_id_comp. Proof. repeat split. - exact (λ (w x y z : B) (v₁ : w -|-> x) (v₂ : y -|-> z) (h₁ h₁' : w --> y) (h₂ : x --> z) (τ : h₁ ==> h₁') (s : square_double_bicat h₁' h₂ v₁ v₂), τ ▵s s). - exact (λ (w x y z : B) (v₁ : w -|-> x) (v₂ : y -|-> z) (h₁ : w --> y) (h₂ h₂' : x --> z) (τ : h₂ ==> h₂') (s : square_double_bicat h₁ h₂ v₁ v₂), τ ▿s s). - exact (λ (w x y z : B) (v₁ v₁' : w -|-> x) (v₂ : y -|-> z) (h₁ : w --> y) (h₂ : x --> z) (τ : v₁ =|=> v₁') (s : square_double_bicat h₁ h₂ v₁' v₂), τ ◃s s). - exact (λ (w x y z : B) (v₁ : w -|-> x) (v₂ v₂' : y -|-> z) (h₁ : w --> y) (h₂ : x --> z) (τ : v₂ =|=> v₂') (s : square_double_bicat h₁ h₂ v₁ v₂), τ ▹s s). 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.DoubleCategories.DoubleBicat.VerityDoubleBicat. Require Import UniMath.Bicategories.DoubleCategories.DoubleBicat.UnderlyingCats.