Proposition square_assoc_v' {C : double_cat} {w₁ w₂ x₁ x₂ y₁ y₂ z₁ z₂ : C} {v₁ : w₁ -->v x₁} {v₁' : x₁ -->v y₁} {v₁'' : y₁ -->v z₁} {v₂ : w₂ -->v x₂} {v₂' : x₂ -->v y₂} {v₂'' : y₂ -->v z₂} {h₁ : w₁ -->h w₂} {h₂ : x₁ -->h x₂} {h₃ : y₁ -->h y₂} {h₄ : z₁ -->h z₂} (s₁ : square v₁ v₂ h₁ h₂) (s₂ : square v₁' v₂' h₂ h₃) (s₃ : square v₁'' v₂'' h₃ h₄) : transportf_square (assoc _ _ _) (assoc _ _ _) (s₁ ⋆v (s₂ ⋆v s₃)) = ((s₁ ⋆v s₂) ⋆v s₃). Proof. rewrite square_assoc_v. rewrite transportfb_square. 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.DerivedLaws.TransportLaws. Require Import UniMath.Bicategories.DoubleCategories.Core.DoubleCats. Require Import UniMath.Bicategories.DoubleCategories.Core.UnivalentDoubleCats.