∀ {G : Type u_1} [inst : Group G] {A B : Subgroup G} (φ : ↥A ≃* ↥B) {d : HNNExtension.NormalWord.TransversalPair G A B}
  (u : ℤˣ) (w : HNNExtension.NormalWord d),
  HNNExtension.NormalWord.unitsSMulWithCancel φ u w =
    HNNExtension.NormalWord.consRecOn (motive := fun x =>
      HNNExtension.NormalWord.Cancels u x → HNNExtension.NormalWord d) w (id fun g a => w) fun g x w x_1 x_2 x_3 can =>
      ↑((HNNExtension.toSubgroupEquiv φ u) ⟨g, ⋯⟩) • w