Proposition transportb_b_square {C : double_cat} {x₁ x₂ y₁ y₂ : C} {v₁ v₁' v₁'' : x₁ -->v y₁} {v₂ v₂' v₂'' : x₂ -->v y₂} {h₁ : x₁ -->h x₂} {h₂ : y₁ -->h y₂} (p₁ : v₁ = v₁') (p₂ : v₁' = v₁'') (q₁ : v₂ = v₂') (q₂ : v₂' = v₂'') (s : square v₁'' v₂'' h₁ h₂) : transportb_square p₁ q₁ (transportb_square p₂ q₂ s) = transportb_square (p₁ @ p₂) (q₁ @ q₂) s. Proof. induction p₁, p₂, q₁, q₂. 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.