∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] (J : CategoryTheory.GrothendieckTopology C)
  [inst_1 : J.Subcanonical] {X Y : Cᵒᵖ} {F : CategoryTheory.Sheaf J (Type (max v v'))}
  (f : (CategoryTheory.GrothendieckTopology.uliftYoneda.{v', v, u} J).obj (Opposite.unop X) ⟶ F) (g : X ⟶ Y),
  F.val.map g (J.uliftYonedaEquiv f) = f.val.app Y { down := g.unop }