∀ (motive : List ℕ → List ℕ → Sort u_1) (x : List ℕ) (h_1 : (x : List ℕ) → motive [] x)
  (h_2 : (x : List ℕ) → motive x [])
  (h_3 : (id₁ : ℕ) → (ids₁ : List ℕ) → (id₂ : ℕ) → (ids₂ : List ℕ) → motive (id₁ :: ids₁) (id₂ :: ids₂)),
  (x = [] → False) →
    (match x, [] with
      | [], x => h_1 x
      | x, [] => h_2 x
      | id₁ :: ids₁, id₂ :: ids₂ => h_3 id₁ ids₁ id₂ ids₂) =
      h_2 x