theorem knockout_cascade_with_weights
{N : ℕ} (hN : 0 < N) (F : Fin N → ℝ)
(hF0 : F ⟨0, hN⟩ = 0)
(hdep : ∀ (i : ℕ) (hi : i < N), 0 < i →
∃ (a : ℝ), F ⟨i, hi⟩ = a * F ⟨i - 1, by omega⟩) :
∀ (i : ℕ) (hi : i < N), F ⟨i, hi⟩ = 0 := by
exact knockout_cascade hN F hF0 hdep## Theorem 4b.6: Weight-Dependent Knockout Cascade