Proposition transportf_s_square_post_whisker_v {C : strict_double_cat} {x₁ x₂ y₁ y₂ z₁ z₂ : C} {v₁ : x₁ -->v y₁} {w₁ w₁' : y₁ --> z₁} {v₂ : x₂ -->v y₂} {w₂ w₂' : y₂ --> z₂} (p : w₁ = w₁') (q : w₂ = w₂') {h₁ : x₁ -->h x₂} {h₂ : y₁ -->h y₂} {k : z₁ -->h z₂} (s₁ : s_square v₁ v₂ h₁ h₂) (s₂ : s_square w₁ w₂ h₂ k) : s₁ ⋆v transportf_s_square p q (idpath _) (idpath _) s₂ = transportf_s_square (maponpaths (λ z, _ ·v z) p) (maponpaths (λ z, _ ·v z) q) (idpath _) (idpath _) (s₁ ⋆v 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.