Proposition horizontal_cell_to_square_to_horizontal_cell (HB : horizontally_saturated B) {x y : B} {h₁ h₂ : x --> y} (τ : h₁ ==> h₂) : square_to_horizontal_cell HB (horizontal_cell_to_square τ) = τ. Proof. apply (homotinvweqweq (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.