Proposition transportb_square_postwhisker {C : double_cat} {x₁ x₂ y₁ y₂ z₁ z₂ : C} {v₁ : x₁ -->v y₁} {v₂ : x₂ -->v y₂} {w₁ w₁' : y₁ -->v z₁} {w₂ w₂' : y₂ -->v z₂} {h₁ : x₁ -->h x₂} {h₂ : y₁ -->h y₂} {k : z₁ -->h z₂} (p : w₁ = w₁') (q : w₂ = w₂') (s : square v₁ v₂ h₁ h₂) (s' : square w₁' w₂' h₂ k) : s ⋆v transportb_square p q s' = transportb_square (maponpaths (λ z, _ ·v z) p) (maponpaths (λ z, _ ·v z) q) (s ⋆v s'). Proof. induction p, q ; cbn. 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.