∀ {σ : Type u_1} {R : Type u_2} [inst : Semiring R] (w : σ → ℕ) {f g : MvPowerSeries σ R},
  min (MvPowerSeries.weightedOrder w f) (MvPowerSeries.weightedOrder w g) ≤ MvPowerSeries.weightedOrder w (f + g)