Proposition rassociator_square' {C : double_cat} {w₁ w₂ x₁ x₂ y₁ y₂ z₁ z₂ : C} {vw : w₁ -->v w₂} {vx : x₁ -->v x₂} {vy : y₁ -->v y₂} {vz : z₁ -->v z₂} {h₁ : w₁ -->h x₁} {h₂ : w₂ -->h x₂} {j₁ : x₁ -->h y₁} {j₂ : x₂ -->h y₂} {k₁ : y₁ -->h z₁} {k₂ : y₂ -->h z₂} (s₁ : square vw vx h₁ h₂) (s₂ : square vx vy j₁ j₂) (s₃ : square vy vz k₁ k₂) : transportb_square (id_v_right _ @ !(id_v_left _)) (id_v_right _ @ !(id_v_left _)) (rassociator_h h₁ j₁ k₁ ⋆v (s₁ ⋆h (s₂ ⋆h s₃))) = ((s₁ ⋆h s₂) ⋆h s₃) ⋆v rassociator_h h₂ j₂ k₂. Proof. rewrite rassociator_square. rewrite transportbf_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.