∀ (p : DyckWord),
  List.count DyckStep.U (List.take ((↑p).length - 1) ↑p) + 1 =
      List.count DyckStep.D (List.take ((↑p).length - 1) ↑p) + 0 →
    List.count DyckStep.D (List.take ((↑p).length - 1) ↑p) ≤ List.count DyckStep.U (List.take ((↑p).length - 1) ↑p) →
      False