∀ {α : Type u_1} {a : α} (motive : (x : List α) → a ∉ x → Prop) (x : List α) (x_1 : a ∉ x),
  (∀ (x : a ∉ []), motive [] x) → (∀ (b : α) (l : List α) (h : a ∉ b :: l), motive (b :: l) h) → motive x x_1