Definition hom_h_hom_h_sq_z_iso_weq : z_iso (C := hom_h B x y) h₁ h₂ ≃ z_iso (C := hom_h_sq B x y) h₁ h₂. Proof. use weq_iso. - exact hom_h_to_hom_h_sq_z_iso. - exact hom_h_sq_to_hom_h_z_iso. - abstract (intro f ; use z_iso_eq ; cbn ; apply horizontal_cell_to_square_to_horizontal_cell). - abstract (intro f ; use z_iso_eq ; cbn ; apply square_to_horizontal_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.