Theorems · Theorem · commutative algebra
MvPowerSeries.ne_zero_iff_weightedOrder_finite
∀ {σ : Type u_1} {R : Type u_2} [inst : Semiring R] (w : σ → ℕ) {f : MvPowerSeries σ R},
f ≠ 0 ↔ ↑(MvPowerSeries.weightedOrder w f).toNat = MvPowerSeries.weightedOrder w f- Defined in
- Mathlib.RingTheory.MvPowerSeries.Order
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 82 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.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Semiringstatement and proof · cited by 13,802
- Finsuppproof · cited by 5,255
- ENatstatement · cited by 4,985
- MvPowerSeriesstatement and proof · cited by 659
- MvPowerSeries.coeffproof · cited by 273
- ENat.toNatstatement · cited by 143
- Nat.findproof · cited by 139
- Finsupp.weightproof · cited by 90
- MvPowerSeries.weightedOrderstatement · cited by 37
Cited by5
Results whose statement or proof uses this declaration.
- MvPowerSeries.exists_coeff_ne_zero_and_weightedOrderproof · cited by 4
- MvPowerSeries.weightedOrder_eq_top_iffproof · cited by 3
- MvPowerSeries.weightedOrder_mulproof · cited by 2
- MvPowerSeries.ne_zero_iff_order_finiteproof · cited by 1
- MvPowerSeries.le_weightedOrder_subst_of_forall_ne_zeroproof · cited by 0