{motive : DyckWord → Sort u} →
  ((toList : List DyckStep) →
      (count_U_eq_count_D : List.count DyckStep.U toList = List.count DyckStep.D toList) →
        (count_D_le_count_U :
            ∀ (i : ℕ), List.count DyckStep.D (List.take i toList) ≤ List.count DyckStep.U (List.take i toList)) →
          motive
            { toList := toList, count_U_eq_count_D := count_U_eq_count_D, count_D_le_count_U := count_D_le_count_U }) →
    (t : DyckWord) → motive t