Proposition transportb_square_eq {C : double_cat} {x₁ x₂ y₁ y₂ : C} {v₁ v₁' : x₁ -->v y₁} {v₂ v₂' : x₂ -->v y₂} {h₁ : x₁ -->h x₂} {h₂ : y₁ -->h y₂} (p p' : v₁ = v₁') (q q' : v₂ = v₂') {s s' : square v₁' v₂' h₁ h₂} (r : s = s') : transportb_square p q s = transportb_square p' q' s'. Proof. assert (t : p = p') by apply isaset_ver_mor. rewrite t ; clear t. assert (t : q = q') by apply isaset_ver_mor. rewrite t ; clear t. apply maponpaths. exact r. 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.