Proposition path_to_globular_iso_to_path {C : univalent_double_cat} {x y : C} {h₁ h₂ : x -->h y} (p : h₁ = h₂) : globular_iso_square_to_path (path_to_globular_iso_square p) = p. Proof. exact (idtoisotoid_twosided_disp (is_univalent_twosided_disp_cat_hor_mor C) (idpath _) (idpath _) p). 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.