Proposition v_sq_isotoid_idtoiso_2_1 {B : verity_double_bicat} (H : vertically_saturated B) (HB_2_1 : ver_locally_univalent B) {x y : B} {v₁ v₂ : x -|-> y} (p : v₁ = v₂) : v_sq_isotoid_2_1 H HB_2_1 (v_sq_idtoiso_2_1 p) = p. Proof. unfold v_sq_idtoiso_2_1, v_sq_isotoid_2_1. etrans. { apply maponpaths. exact (homotweqinvweq (vertical_square_weq_invertible_2cell H v₁ v₂) (idtoiso_2_1 v₁ v₂ p)). } apply isotoid_2_1_idtoiso_2_1. 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.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.