Theorems · Theorem · commutative algebra
MvPowerSeries.le_order
∀ {σ : Type u_1} {R : Type u_2} [inst : Semiring R] {f : MvPowerSeries σ R} {n : ℕ∞},
(∀ (d : σ →₀ ℕ), ↑(Finsupp.degree d) < n → (MvPowerSeries.coeff d) f = 0) → n ≤ f.orderThe order of a formal power series is at least n if
the dth coefficient is 0 for all d such that degree d < n.
- Defined in
- Mathlib.RingTheory.MvPowerSeries.Order
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 86 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 and proof · cited by 4,985
- AddMonoidHomstatement · cited by 3,230
- MvPowerSeriesstatement and proof · cited by 659
- MvPowerSeries.coeffstatement and proof · cited by 273
- Finsupp.degreestatement and proof · cited by 94
- MvPowerSeries.orderstatement · cited by 45
- Finsupp.degree_eq_weight_oneproof · cited by 26
Cited by4
Results whose statement or proof uses this declaration.
- PowerSeries.order_eq_orderproof · cited by 4
- MvPowerSeries.one_le_order_iff_constCoeff_eq_zeroproof · cited by 2
- MvPowerSeries.order_expandproof · cited by 1
- MvPowerSeries.order_toSubringproof · cited by 0