∀ {ι : Type u_2} {G : ι → Type u_3} {H : Type u_4} [inst : (i : ι) → Group (G i)] [inst_1 : Group H]
  {φ : (i : ι) → H →* G i} {d : Monoid.PushoutI.NormalWord.Transversal φ} [inst_2 : DecidableEq ι]
  [inst_3 : (i : ι) → DecidableEq (G i)] {motive : Monoid.PushoutI.NormalWord d → Sort u_1} (w : Monoid.CoprodI.Word G)
  (head : H) (h3 : ∀ (i : ι) (g : G i), ⟨i, g⟩ ∈ w.toList → g ∈ d.set i),
  motive { toWord := w, head := head, normalized := h3 } =
    motive ((Monoid.PushoutI.base φ) head • { toWord := w, head := 1, normalized := h3 })