Theorems · Theorem · commutative algebra
MvPowerSeries.order_le
∀ {σ : Type u_1} {R : Type u_2} [inst : Semiring R] {f : MvPowerSeries σ R} {d : σ →₀ ℕ},
(MvPowerSeries.coeff d) f ≠ 0 → f.order ≤ ↑(Finsupp.degree d)If the dth coefficient of a formal power series is nonzero,
then the order of the power series is less than or equal to degree d.
- Defined in
- Mathlib.RingTheory.MvPowerSeries.Order
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 84 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.
Cites13
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
- Finsuppstatement and proof · cited by 5,255
- ENatstatement · cited by 4,985
- AddMonoidHomstatement and proof · cited by 3,230
- MvPowerSeriesstatement and proof · cited by 659
- MvPowerSeries.coeffstatement and proof · cited by 273
- Finsupp.degreestatement · cited by 94
- MvPowerSeries.orderstatement and proof · cited by 45
- Finsupp.degree_eq_weight_oneproof · cited by 26
Cited by2
Results whose statement or proof uses this declaration.
- MvPowerSeries.le_order_substproof · cited by 1
- MvPowerSeries.order_expandproof · cited by 1