{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} →
            [SizeOf ι] → [(a : ι) → SizeOf (G a)] → [SizeOf H] → Monoid.PushoutI.NormalWord.Transversal φ → ℕ