Definition comp_diag_ul_corner {B : verity_double_bicat} {x y z : B} {v₁ : x -|-> y} {v₂ : y -|-> z} {h₁ : x --> y} {h₂ : y --> z} (s₁ : square_double_bicat (id_h x) h₁ (id_v x) v₁) (s₂ : square_double_bicat (id_h y) h₂ (id_v y) v₂) : square_double_bicat (id_h x) (h₁ · h₂) (id_v x) (v₁ · v₂) := linvunitor _ ◃s (linvunitor _ ▵s ((s₁ ⋆h id_h_square_bicat _) ⋆v (id_v_square_bicat h₁ ⋆h s₂))).
Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.TwoSidedDispCat. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Isos. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Univalence. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Discrete. 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.DoubleCategories.DoubleBicat.VerityDoubleBicat.