∀ {ι : Type u_1} {G : ι → Type u_2} {H : Type u_3} [inst : (i : ι) → Group (G i)] [inst_1 : Group H]
  {φ : (i : ι) → H →* G i} {d : Monoid.PushoutI.NormalWord.Transversal φ} (h : H) (w : Monoid.PushoutI.NormalWord d),
  h • w = { toWord := w.toWord, head := h * w.head, normalized := ⋯ }