{G : Type u_1} →
  [inst : Group G] →
    {A B : Subgroup G} →
      G →
        (toList : List (ℤˣ × G)) →
          List.IsChain (fun a b => a.2 ∈ HNNExtension.toSubgroup A B a.1 → a.1 = b.1) toList →
            HNNExtension.NormalWord.ReducedWord G A B