∀ {M : Type u_1} [inst : AddCommGroup M] [inst_1 : LinearOrder M] [inst_2 : IsOrderedAddMonoid M] {a b : M}
  (motive : ArchimedeanClass.mk a ≤ ArchimedeanClass.mk b → Prop) (x : ArchimedeanClass.mk a ≤ ArchimedeanClass.mk b),
  (∀ (n : ℕ) (hn : |ArchimedeanOrder.val (ArchimedeanOrder.of b)| ≤ n • |ArchimedeanOrder.val (ArchimedeanOrder.of a)|),
      motive ⋯) →
    motive x