Theorems · Theorem · commutative algebra
MvPowerSeries.ne_zero_iff_order_finite
∀ {σ : Type u_1} {R : Type u_2} [inst : Semiring R] {f : MvPowerSeries σ R}, f ≠ 0 ↔ ↑f.order.toNat = f.order- Defined in
- Mathlib.RingTheory.MvPowerSeries.Order
- Cited by
- 1 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.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- ENatstatement · cited by 4,985
- MvPowerSeriesstatement and proof · cited by 659
- ENat.toNatstatement · cited by 143
- MvPowerSeries.orderstatement · cited by 45
- MvPowerSeries.ne_zero_iff_weightedOrder_finiteproof · cited by 5
Cited by1
Results whose statement or proof uses this declaration.
- MvPowerSeries.order_expandproof · cited by 1