proposition: 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: 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.
imports: UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Prelude UniMath.CategoryTheory.Core.Setcategories UniMath.CategoryTheory.Categories.CategoryOfSetCategories UniMath.CategoryTheory.PrecategoryBinProduct UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Functors UniMath.CategoryTheory.DisplayedCats.NaturalTransformations UniMath.CategoryTheory.DisplayedCats.Isos UniMath.CategoryTheory.DisplayedCats.Total UniMath.CategoryTheory.DisplayedCats.Univalence UniMath.CategoryTheory.DisplayedCats.Constructions UniMath.CategoryTheory.DisplayedCats.DisplayedCatEq UniMath.CategoryTheory.DisplayedCats.Examples.DispFunctorPair UniMath.CategoryTheory.TwoSidedDisplayedCats.TwoSidedDispCat UniMath.CategoryTheory.TwoSidedDisplayedCats.DisplayedFunctor UniMath.CategoryTheory.TwoSidedDisplayedCats.DisplayedNatTrans UniMath.CategoryTheory.TwoSidedDisplayedCats.Isos UniMath.CategoryTheory.TwoSidedDisplayedCats.Univalence UniMath.CategoryTheory.TwoSidedDisplayedCats.Strictness UniMath.CategoryTheory.TwoSidedDisplayedCats.TransportLaws