Proposition transportf_f_s_square {C : strict_double_cat} {x₁ x₂ y₁ y₂ : C} {v₁ v₁' v₁'' : x₁ -->v y₁} {v₂ v₂' v₂'' : x₂ -->v y₂} {h₁ h₁' h₁'' : x₁ -->h x₂} {h₂ h₂' h₂'' : y₁ -->h y₂} (s : s_square v₁ v₂ h₁ h₂) (p₁ : v₁ = v₁') (q₁ : v₁' = v₁'') (p₂ : v₂ = v₂') (q₂ : v₂' = v₂'') (p₃ : h₁ = h₁') (q₃ : h₁' = h₁'') (p₄ : h₂ = h₂') (q₄ : h₂' = h₂'') : transportf_s_square q₁ q₂ q₃ q₄ (transportf_s_square p₁ p₂ p₃ p₄ s) = transportf_s_square (p₁ @ q₁) (p₂ @ q₂) (p₃ @ q₃) (p₄ @ q₄) s. Proof. induction p₁, p₂, p₃, p₄, q₁, q₂, q₃, q₄ ; 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.