Proposition path_to_globular_iso_square_comp {C : univalent_double_cat} {x y : C} {h₁ h₂ h₃ : x -->h y} (p : h₁ = h₂) (q : h₂ = h₃) : transportf_square (id_v_left _) (id_v_left _) (path_to_globular_iso_square p ⋆v path_to_globular_iso_square q) = path_to_globular_iso_square (p @ q). Proof. induction p, q. rewrite <- !path_to_globular_iso_square_id. rewrite square_id_left_v. rewrite transportfb_square. apply idpath. Qed.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.TwoSidedDispCat. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Univalence. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.DoubleCategories.Core.DoubleCats. Require Import UniMath.Bicategories.DoubleCategories.DerivedLaws.TransportLaws. Require Import UniMath.Bicategories.DoubleCategories.Core.DoubleCats. Require Import UniMath.Bicategories.DoubleCategories.Core.UnivalentDoubleCats.