Proposition transportb_disp_cat_of_strict_twosided_disp_cat_ob {C₁ C₂ : setcategory} {D₁ : twosided_disp_cat C₁ C₁} {D₂ : twosided_disp_cat C₂ C₂} (FD : functor_data C₁ C₂) (HF₁ HF₂ : is_functor FD) (F := make_functor FD HF₁) (G := make_functor FD HF₂) (p : F = G) (GG : twosided_disp_functor G G D₁ D₂) {x y : C₁} (xy : D₁ x y) : (transportb (λ H, twosided_disp_functor H H D₁ D₂) p GG) x y xy = GG x y xy. Proof. etrans. { apply transportb_disp_cat_of_strict_twosided_disp_cat_ob_help. } assert (path_functor_ob p x = idpath _) as r₁. { apply isaset_ob. } assert (path_functor_ob p y = idpath _) as r₂. { apply isaset_ob. } rewrite r₁, r₂. 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.PrecategoryBinProduct. 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.DisplayedCatEq. Require Import UniMath.CategoryTheory.DisplayedCats.Examples.DispFunctorPair. 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. Section FromIso. End FromIso.