{α : Type u_1} →
  (p : α → Prop) →
    (motive : (x : List α) → (∃ a ∈ x, p a) → Sort u_2) →
      (x : List α) →
        (x_1 : ∃ a ∈ x, p a) →
          ((hp : ∃ a ∈ [], p a) → motive [] hp) →
            ((l : α) → (ls : List α) → (hp : ∃ a ∈ l :: ls, p a) → motive (l :: ls) hp) → motive x x_1