∀ {α : Type u_1} [inst : AddCommMonoid α] [inst_1 : IsCancelAdd α] {s : AddSubmonoid α} [inst_2 : DecidableEq α]
  (a b : AddLocalization s),
  a.decidableEq b = a.recOnSubsingleton₂ b fun x x_1 x_2 x_3 => decidable_of_iff' (↑x_3 + x = ↑x_2 + x_1) ⋯