∀ {α : Type u_1} {β : Type u_2} [inst : Field α] [inst_1 : LinearOrder α] {abv : β → α} {g : ℕ → β}
  (motive : (∃ r > 0, ∀ (i : ℕ), abv (g i) < r) → Prop) (x : ∃ r > 0, ∀ (i : ℕ), abv (g i) < r),
  (∀ (w : α) (left : w > 0) (hG : ∀ (i : ℕ), abv (g i) < w), motive ⋯) → motive x