Proposition transportf_s_square_post_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 : x₁ -->h y₁) (h₂ : x₂ -->h y₂) {k₁ k₁' : y₁ -->h z₁} (p : k₁ = k₁') {k₂ k₂' : y₂ -->h z₂} (q : k₂ = k₂') (s₁ : s_square vx vy h₁ h₂) (s₂ : s_square vy vz k₁ k₂) : s₁ ⋆h transportf_s_square (idpath _) (idpath _) p q s₂ = transportf_s_square (idpath _) (idpath _) (maponpaths (λ z, _ ·h z) p) (maponpaths (λ z, _ ·h z) 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.