∀ {G : Type u_1} [inst : Group G] {A B : Subgroup G} {d : HNNExtension.NormalWord.TransversalPair G A B}
  [inst_1 : SizeOf G] (toReducedWord : HNNExtension.NormalWord.ReducedWord G A B)
  (mem_set : ∀ (u : ℤˣ) (g : G), (u, g) ∈ toReducedWord.toList → g ∈ d.set u),
  sizeOf { toReducedWord := toReducedWord, mem_set := mem_set } = 1 + sizeOf toReducedWord