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