∀ {C : Type u_2} [inst : CategoryTheory.Category.{u_1, u_2} C] [inst_1 : CategoryTheory.MonoidalCategory C]
  (P : CategoryTheory.ObjectProperty C),
  (∀ (X Y : C), P X → P Y → P (CategoryTheory.MonoidalCategoryStruct.tensorObj X Y)) →
    ∀ (X Y : P.FullSubcategory), P (CategoryTheory.MonoidalCategoryStruct.tensorObj X.obj Y.obj)