∀ {G : Type u_1} [inst : Group G] {A B : Subgroup G} (φ : ↥A ≃* ↥B) (d : HNNExtension.NormalWord.TransversalPair G A B)
  (w : HNNExtension.NormalWord d),
  (fun g => g • HNNExtension.NormalWord.empty)
      ((fun w => HNNExtension.NormalWord.ReducedWord.prod φ w.toReducedWord) w) =
    w