proposition: Lemma fourth_iso_nat_in_x (F : PreShv C) : is_nat_trans (pr1 (Fun3 F)) _ (λ x, fourth_iso_on_sets F x).
proof: Proof. intros X Y f. use (is_natural_yoneda_iso _ _ _ _ (BinProduct_of_functors_mor _ _ PC _ _ _ _ _)). Qed.
imports: UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Limits.BinProducts UniMath.CategoryTheory.exponentials UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.opp_precat UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.RightKanExtension UniMath.CategoryTheory.Adjunctions.Core UniMath.CategoryTheory.yoneda UniMath.CategoryTheory.YonedaBinproducts UniMath.CategoryTheory.Categories.HSET.Core UniMath.CategoryTheory.Categories.HSET.Limits UniMath.CategoryTheory.Categories.HSET.Structures UniMath.CategoryTheory.Categories.HSET.MonoEpiIso UniMath.CategoryTheory.Limits.Graphs.Limits UniMath.CategoryTheory.Presheaf