Theorems · Theorem · commutative algebra
MvPowerSeries.weightedOrder_le
∀ {σ : Type u_1} {R : Type u_2} [inst : Semiring R] (w : σ → ℕ) {f : MvPowerSeries σ R} {d : σ →₀ ℕ},
(MvPowerSeries.coeff d) f ≠ 0 → MvPowerSeries.weightedOrder w f ≤ ↑((Finsupp.weight w) d)If the dth coefficient of a formal power series is nonzero,
then the weighted order of the power series is less than or equal to weight d w.
- Defined in
- Mathlib.RingTheory.MvPowerSeries.Order
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 83 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
- le_rflproof · cited by 1,558
- MvPowerSeriesstatement and proof · cited by 659
- MvPowerSeries.coeffstatement and proof · cited by 273
- Finsupp.weightstatement and proof · cited by 90
- MvPowerSeries.weightedOrderstatement · cited by 37
Cited by4
Results whose statement or proof uses this declaration.
- MvPowerSeries.coeff_eq_zero_of_lt_weightedOrderproof · cited by 14
- MvPowerSeries.order_leproof · cited by 2
- MvPowerSeries.weightedOrder_eq_natproof · cited by 2
- MvPowerSeries.le_weightedOrder_subst_of_forall_ne_zeroproof · cited by 0