∀ {α : Type u_1} [inst : CommMonoid α] [inst_1 : PartialOrder α] [inst_2 : IsOrderedCancelMonoid α] {s : Submonoid α}
  {a₁ b₁ : α} {a₂ b₂ : ↥s}, (Localization.mk a₁ a₂ ≤ Localization.mk b₁ b₂) = (↑b₂ * a₁ ≤ ↑a₂ * b₁)