Proposition square_to_horizontal_cell_to_square (HB : horizontally_saturated B) {x y : B} {h₁ h₂ : x --> y} (s : square_double_bicat h₁ h₂ (id_v x) (id_v y)) : horizontal_cell_to_square (square_to_horizontal_cell HB s) = s. Proof. apply (homotweqinvweq (horizontal_cell_to_square_weq HB h₁ h₂)). 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.