∀ {α : Type u_1} {p q : α → Bool} (motive : (x : List α) → (∀ x_1 ∈ x, p x_1 = q x_1) → Prop) (x : List α)
  (x_1 : ∀ x_1 ∈ x, p x_1 = q x_1),
  (∀ (x : ∀ x ∈ [], p x = q x), motive [] x) →
    (∀ (a : α) (l : List α) (h : ∀ x ∈ a :: l, p x = q x), motive (a :: l) h) → motive x x_1