Proposition transportf_s_square_pre_whisker_v' {C : strict_double_cat} {x₁ x₂ y₁ y₂ z₁ z₂ : C} {v₁ v₁' : x₁ -->v y₁} {w₁ : y₁ --> z₁} {v₂ v₂' : x₂ -->v y₂} {w₂ : y₂ --> z₂} (p₁ : v₁ = v₁') (p₂ : v₂ = v₂') {h₁ h₁' : x₁ -->h x₂} (p₃ : h₁ = h₁') {h₂ h₂' : y₁ -->h y₂} (p₄ : h₂ = h₂') {k k' : z₁ -->h z₂} (r : k = k') (s₁ : s_square v₁ v₂ h₁ h₂) (s₂ : s_square w₁ w₂ h₂' k') : transportf_s_square p₁ p₂ p₃ p₄ s₁ ⋆v s₂ = transportf_s_square (maponpaths (λ z, z ·v _) p₁) (maponpaths (λ z, z ·v _) p₂) p₃ r (s₁ ⋆v transportf_s_square (idpath _) (idpath _) (!p₄) (!r) 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.