Proposition transportf_square_id_h_square_eq {C : double_cat} {x y : C} {v₁ v₂ w₁ w₂ : x -->v y} (p₁ : v₁ = w₁) (p₂ : v₂ = w₁) (q₁ : v₁ = w₂) (q₂ : v₂ = w₂) : transportf_square p₁ q₁ (id_h_square v₁) = transportf_square p₂ q₂ (id_h_square v₂). Proof. induction p₁, p₂, q₁. assert (idpath _ = q₂) as r. { apply isaset_ver_mor. } induction r. 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.Univalence. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.DoubleCategories.Core.DoubleCats. Require Import UniMath.Bicategories.DoubleCategories.Core.UnivalentDoubleCats.