Definition path_weq_globular_iso_square {C : univalent_double_cat} {x y : C} (h₁ h₂ : x -->h y) : h₁ = h₂ ≃ globular_iso_square h₁ h₂. Proof. use weq_iso. - apply path_to_globular_iso_square. - apply globular_iso_square_to_path. - apply path_to_globular_iso_to_path. - apply globular_iso_to_path_to_iso. Defined.
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.