Proposition transportb_square_id {C : double_cat} {x₁ x₂ y₁ y₂ : C} {v₁ : x₁ -->v y₁} {v₂ : x₂ -->v y₂} {h₁ : x₁ -->h x₂} {h₂ : y₁ -->h y₂} (p : v₁ = v₁) (q : v₂ = v₂) (s : square v₁ v₂ h₁ h₂) : transportb_square p q s = s. Proof. assert (r : p = idpath _) by apply isaset_ver_mor. rewrite r ; clear r. assert (r : q = idpath _) by apply isaset_ver_mor. rewrite r ; clear 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.