Proposition transportf_s_square_pre_whisker_h {C : strict_double_cat} {x₁ x₂ y₁ y₂ z₁ z₂ : C} {vx : x₁ -->v x₂} {vy : y₁ -->v y₂} {vz : z₁ -->v z₂} {h₁ h₁' : x₁ -->h y₁} (p : h₁ = h₁') {h₂ h₂' : x₂ -->h y₂} (q : h₂ = h₂') (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 (idpath _) (idpath _) p q s₁ ⋆h s₂ = transportf_s_square (idpath _) (idpath _) (maponpaths (λ z, z ·h _) p) (maponpaths (λ z, z ·h _) q) (s₁ ⋆h s₂). Proof. induction p, q ; 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.