Proposition h_sq_isotoid_idtoiso_2_1 {B : verity_double_bicat} (H : horizontally_saturated B) (HB_2_1 : hor_locally_univalent B) {x y : B} {h₁ h₂ : x --> y} (p : h₁ = h₂) : h_sq_isotoid_2_1 H HB_2_1 (h_sq_idtoiso_2_1 p) = p. Proof. unfold h_sq_idtoiso_2_1, h_sq_isotoid_2_1. etrans. { apply maponpaths. exact (homotweqinvweq (horizontal_square_weq_invertible_2cell H h₁ h₂) (idtoiso_2_1 h₁ h₂ 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.