∀ {I : Type u} {f : I → Type v₁} [inst : (i : I) → AddMonoid (f i)],
  Pi.addMonoid =
    { toAddSemigroup := Pi.addSemigroup, toZero := Pi.addZeroClass.toZero, zero_add := ⋯, add_zero := ⋯,
      nsmul := fun n x i => n • x i, nsmul_zero := ⋯, nsmul_succ := ⋯ }