Proposition strict_square_assoc {C : strict_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 : x₁ -->h y₁} {h₃ : y₁ -->h z₁} {k₁ : w₂ -->h x₂} {k₂ : x₂ -->h y₂} {k₃ : y₂ -->h z₂} (s₁ : s_square vw vx h₁ k₁) (s₂ : s_square vx vy h₂ k₂) (s₃ : s_square vy vz h₃ k₃) : s₁ ⋆h (s₂ ⋆h s₃) = transportb_s_square (idpath _) (idpath _) (s_assocl_h _ _ _) (s_assocl_h _ _ _) ((s₁ ⋆h s₂) ⋆h s₃). Proof. apply (pr222 (pr222 C) w₁ w₂ x₁ x₂ y₁ y₂ z₁ z₂ vw vx vy vz h₁ h₂ h₃ k₁ k₂ k₃ s₁ s₂ s₃). Defined.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.Core.Setcategories. Require Import UniMath.CategoryTheory.Categories.CategoryOfSetCategories. Require Import UniMath.CategoryTheory.whiskering. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Functors. Require Import UniMath.CategoryTheory.DisplayedCats.NaturalTransformations. Require Import UniMath.CategoryTheory.DisplayedCats.Isos. Require Import UniMath.CategoryTheory.DisplayedCats.Total. Require Import UniMath.CategoryTheory.DisplayedCats.Univalence. Require Import UniMath.CategoryTheory.DisplayedCats.Constructions. Require Import UniMath.CategoryTheory.DisplayedCats.Examples.StrictTwoSidedDispCat. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.TwoSidedDispCat. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.DisplayedFunctor. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.DisplayedNatTrans. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Isos. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Univalence. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Strictness. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.TransportLaws. Require Import UniMath.Bicategories.DoubleCategories.Basics.DoubleCategoryBasics. Require Import UniMath.Bicategories.DoubleCategories.Basics.StrictDoubleCatBasics. Require Import UniMath.Bicategories.DoubleCategories.Core.CatOfStrictDoubleCats.