Theorems · Theorem · commutative algebra

MvPowerSeries.le_weightedOrder

∀ {σ : Type u_1} {R : Type u_2} [inst : Semiring R] (w : σ → ℕ) {f : MvPowerSeries σ R} {n : ℕ∞},
  (∀ (d : σ →₀ ℕ), ↑((Finsupp.weight w) d) < n → (MvPowerSeries.coeff d) f = 0) → n ≤ MvPowerSeries.weightedOrder w f

The order of a formal power series is at least n if the dth coefficient is 0 for all d such that weight w d < n.

Defined in

Mathlib.RingTheory.MvPowerSeries.Order

Cited by

7 results in Mathlib

Foundations

Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

Semiring