∀ {w : ℕ} (motive : (s : ℕ) → s < w → 0 < s → Sort u_1) (hs : 0 < w) (hslt : 0 < 0)
  (h_1 : (hs : 0 < w) → (hslt : 0 < 0) → 0 = 0 → motive 0 hs hslt)
  (h_2 : (s' : ℕ) → (hs : s' + 1 < w) → (hslt : 0 < s' + 1) → 0 = s'.succ → motive s'.succ hs hslt),
  (match hs0 : 0, hs, hslt with
    | 0, hs, hslt => h_1 hs hslt hs0
    | s'.succ, hs, hslt => h_2 s' hs hslt hs0) =
    h_1 hs hslt ⋯