Proposition transportf_s_square_eq {C : strict_double_cat} {x₁ x₂ y₁ y₂ : C} {v₁ v₁' : x₁ -->v y₁} {v₂ v₂' : x₂ -->v y₂} {h₁ h₁' : x₁ -->h x₂} {h₂ h₂' : y₁ -->h y₂} {s s' : s_square v₁ v₂ h₁ h₂} (q : s = s') (p₁ p₁' : v₁ = v₁') (p₂ p₂' : v₂ = v₂') (p₃ p₃' : h₁ = h₁') (p₄ p₄' : h₂ = h₂') : transportf_s_square p₁ p₂ p₃ p₄ s = transportf_s_square p₁' p₂' p₃' p₄' s'. Proof. assert (p₁ = p₁') as r by apply isaset_ver_mor_strict_double_cat. induction r. assert (p₂ = p₂') as r by apply isaset_ver_mor_strict_double_cat. induction r. assert (p₃ = p₃') as r by apply isaset_hor_mor_strict_double_cat. induction r. assert (p₄ = p₄') as r by apply isaset_hor_mor_strict_double_cat. induction r. induction p₁, p₂, p₃, p₄ ; cbn. exact q. 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.