Proposition transportf_s_square_pre_whisker_h' {C : strict_double_cat} {x₁ x₂ y₁ y₂ z₁ z₂ : C} {vx vx' : x₁ -->v x₂} (p₁ : vx = vx') {vy vy' : y₁ -->v y₂} (p₂ : vy = vy') {vz vz' : z₁ -->v z₂} {h₁ h₁' : x₁ -->h y₁} (p₃ : h₁ = h₁') {h₂ h₂' : x₂ -->h y₂} (p₄ : h₂ = h₂') (r : vz = vz') (k₁ : y₁ -->h z₁) (k₂ : y₂ -->h z₂) (s₁ : s_square vx vy h₁ h₂) (s₂ : s_square vy' vz k₁ k₂) : transportf_s_square p₁ p₂ p₃ p₄ s₁ ⋆h s₂ = transportf_s_square p₁ (!r) (maponpaths (λ z, z ·h _) p₃) (maponpaths (λ z, z ·h _) p₄) (s₁ ⋆h transportf_s_square (!p₂) r (idpath _) (idpath _) s₂). Proof. induction p₁, p₂, p₃, p₄, r ; cbn. apply idpath. Qed.
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.