∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] {P : CategoryTheory.ObjectProperty C}
  [CategoryTheory.Limits.HasFiniteProducts C] [P.IsClosedUnderLimitsOfShape (CategoryTheory.Discrete PEmpty.{1})]
  [P.IsClosedUnderBinaryProducts], P.IsClosedUnderFiniteProducts