∀ (x : ONote),
  x.fastGrowing =
    let o := x;
    match (motive := (x : Option ONote ⊕ (ℕ → ONote)) → o.FundamentalSequenceProp x → ℕ → ℕ) o.fundamentalSequence,
      ⋯ with
    | Sum.inl none, x => Nat.succ
    | Sum.inl (some a), h =>
      have this := ⋯;
      fun i => a.fastGrowing^[i] i
    | Sum.inr f, h => fun i =>
      have this := ⋯;
      (f i).fastGrowing i