Theorems · Theorem · commutative algebra
PowerSeries.le_order_pow_of_constantCoeff_eq_zero
∀ {R : Type u_1} [inst : Semiring R] {φ : PowerSeries R} (n : ℕ), PowerSeries.constantCoeff φ = 0 → ↑n ≤ (φ ^ n).order- Defined in
- Mathlib.RingTheory.PowerSeries.Order
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 97 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.
Cites12
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
- LE.le.transproof · cited by 3,151
- PowerSeriesstatement and proof · cited by 797
- nsmul_eq_mulproof · cited by 369
- PowerSeries.constantCoeffstatement and proof · cited by 126
- PowerSeries.orderstatement and proof · cited by 92
- le_mul_of_one_le_right'proof · cited by 17
- PowerSeries.one_le_order_iff_constCoeff_eq_zeroproof · cited by 2
- PowerSeries.le_order_powproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- PowerSeries.HasSubst.eventually_coeff_pow_eq_zeroproof · cited by 1