Proposition square_to_vertical_cell_id (HB : vertically_saturated B) {x y : B} (v : x -|-> y) : square_to_vertical_cell HB (id_h_square_bicat v) = id2 v. Proof. use (invmaponpathsweq (vertical_cell_to_square_weq HB v v)) ; cbn. rewrite square_to_vertical_cell_to_square. rewrite vertical_cell_to_square_id. apply idpath. 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.