∀ {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} [inst_2 : SizeOf ι] [inst_3 : (a : ι) → SizeOf (G a)] [inst_4 : SizeOf H]
  (injective : ∀ (i : ι), Function.Injective ⇑(φ i)) (set : (i : ι) → Set (G i)) (one_mem : ∀ (i : ι), 1 ∈ set i)
  (compl : ∀ (i : ι), Subgroup.IsComplement (↑(φ i).range) (set i)),
  sizeOf { injective := injective, set := set, one_mem := one_mem, compl := compl } = 1