∀ {α : Type u_1} [inst : CommMonoid α] [inst_1 : PartialOrder α] [inst_2 : IsOrderedCancelMonoid α] {s : Submonoid α}
  [inst_3 : DecidableLT α] (a b : Localization s),
  a.decidableLT b = a.recOnSubsingleton₂ b fun x x_1 x_2 x_3 => decidable_of_iff' (↑x_3 * x < ↑x_2 * x_1) ⋯