∀ {α : Type u_1} (motive : (x : List α) → List α → x.Nodup → Prop) (x x_1 : List α) (x_2 : x.Nodup),
  (∀ (l₁ : List α) (x : l₁.Nodup), motive l₁ [] x) →
    (∀ (l₁ : List α) (a : α) (l₂ : List α) (hl₁ : l₁.Nodup), motive l₁ (a :: l₂) hl₁) → motive x x_1 x_2