Definition hom_v_hom_v_sq_z_iso_weq : z_iso (C := hom_v B x y) v₁ v₂ ≃ z_iso (C := hom_v_sq B x y) v₁ v₂. Proof. use weq_iso. - exact hom_v_to_hom_v_sq_z_iso. - exact hom_v_sq_to_hom_v_z_iso. - abstract (intro f ; use z_iso_eq ; cbn ; apply vertical_cell_to_square_to_vertical_cell). - abstract (intro f ; use z_iso_eq ; cbn ; apply square_to_vertical_cell_to_square). Defined.
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.Univalence. Require Import UniMath.Bicategories.DoubleCategories.DoubleBicat.VerityDoubleBicat. Require Import UniMath.Bicategories.DoubleCategories.DoubleBicat.DerivedLaws. Require Import UniMath.Bicategories.DoubleCategories.DoubleBicat.UnderlyingCats. Require Import UniMath.Bicategories.DoubleCategories.DoubleBicat.CellsAndSquares.