∀ {α : Type u_2} {β : Type u_3} [inst : DecidableEq α] [inst_1 : AddMonoid α] [inst_2 : DecidableEq β]
  [inst_3 : AddMonoid β] (s : Finset α) (t : Finset β), addRothNumber s * addRothNumber t ≤ addRothNumber (s ×ˢ t)