proposition: Proposition transportb_disp_cat_of_strict_twosided_disp_cat_mor_path {C₁ C₂ : setcategory} {F G : C₁ ⟶ C₂} (p : F = G) {x₁ x₂ : C₁} (f : x₁ --> x₂) : idtoiso (idpath (F x₁)) · idtoiso (path_functor_ob p x₁) · # G f · idtoiso (! path_functor_ob p x₂) · idtoiso (idpath (F x₂)) = # F f.
proof: Proof. induction p ; cbn. rewrite !id_left. rewrite !id_right. 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