∀ {σ : Type u_1} {R : Type u_2} [inst : Semiring R] {f : MvPowerSeries σ R} {n : ℕ},
  f.order = ↑n ↔
    (∃ d, (MvPowerSeries.coeff d) f ≠ 0 ∧ Finsupp.degree d = n) ∧
      ∀ (d : σ →₀ ℕ), Finsupp.degree d < n → (MvPowerSeries.coeff d) f = 0