Theorems · Theorem · commutative algebra
MvPowerSeries.order_ne_zero_iff_constCoeff_eq_zero
∀ {σ : Type u_1} {R : Type u_2} [inst : Semiring R] {f : MvPowerSeries σ R},
f.order ≠ 0 ↔ MvPowerSeries.constantCoeff f = 0- Defined in
- Mathlib.RingTheory.MvPowerSeries.Order
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 95 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.
Cites9
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
- Semiringstatement and proof · cited by 13,802
- RingHomstatement · cited by 10,189
- ENatstatement · cited by 4,985
- MvPowerSeriesstatement and proof · cited by 659
- MvPowerSeries.constantCoeffstatement and proof · cited by 98
- MvPowerSeries.orderstatement · cited by 45
- Order.one_le_iff_ne_zeroproof · cited by 32
- MvPowerSeries.one_le_order_iff_constCoeff_eq_zeroproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- MvPowerSeries.WithPiTopology.summable_pow_of_constantCoeff_eq_zeroproof · cited by 3
- PowerSeries.le_order_subst_leftproof · cited by 1