Theorems · Theorem · commutative algebra
PowerSeries.coeff_order
∀ {R : Type u_1} [inst : Semiring R] {φ : PowerSeries R}, φ ≠ 0 → (PowerSeries.coeff φ.order.toNat) φ ≠ 0If the order of a formal power series is finite, then the coefficient indexed by the order is nonzero.
- Defined in
- Mathlib.RingTheory.PowerSeries.Order
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Semiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- RingHom.idstatement · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- LinearMapstatement · cited by 10,215
- Top.topproof · cited by 9,680
- PowerSeriesstatement and proof · cited by 797
- PowerSeries.coeffstatement and proof · cited by 324
- ENat.toNatstatement and proof · cited by 143
- Nat.findproof · cited by 139
- PowerSeries.orderstatement · cited by 92
- Nat.find_specproof · cited by 74
Cited by4
Results whose statement or proof uses this declaration.
- PowerSeries.IsWeierstrassDivisor.of_map_ne_zeroproof · cited by 11
- PowerSeries.order_mulproof · cited by 2
- PowerSeries.order_eq_emultiplicity_Xproof · cited by 0
- PowerSeries.constantCoeff_divXPowOrder_eq_zero_iffproof · cited by 0