Proposition square_to_vertical_cell_to_square (HB : vertically_saturated B) {x y : B} {v₁ v₂ : x -|-> y} (s : square_double_bicat (id_h x) (id_h y) v₁ v₂) : vertical_cell_to_square (square_to_vertical_cell HB s) = s. Proof. apply (homotweqinvweq (vertical_cell_to_square_weq HB v₁ v₂)). Qed.
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.Unitors. Require Import UniMath.Bicategories.DoubleCategories.DoubleBicat.VerityDoubleBicat. Require Import UniMath.Bicategories.DoubleCategories.DoubleBicat.DerivedLaws.