∀ {α : Type u_1} {β : Type u_2} [inst : LinearOrder α] [inst_1 : Ring β] {abv : β → α} {f g : ℕ → β} (w : α) (i : ℕ)
  (motive : ((∀ k ≥ i, abv (f k - f i) < w) ∧ ∀ k ≥ i, abv (g k - g i) < w) → Prop)
  (x : (∀ k ≥ i, abv (f k - f i) < w) ∧ ∀ k ≥ i, abv (g k - g i) < w),
  (∀ (H₁ : ∀ k ≥ i, abv (f k - f i) < w) (H₂ : ∀ k ≥ i, abv (g k - g i) < w), motive ⋯) → motive x