Theorems · Theorem · commutative algebra
PowerSeries.one_le_order_iff_constCoeff_eq_zero
∀ {R : Type u_1} [inst : Semiring R] {φ : PowerSeries R}, 1 ≤ φ.order ↔ PowerSeries.constantCoeff φ = 0- Defined in
- Mathlib.RingTheory.PowerSeries.Order
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 96 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.
Cites14
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 and proof · cited by 4,985
- PowerSeriesstatement and proof · cited by 797
- CharP.cast_eq_zeroproof · cited by 357
- PowerSeries.coeffproof · cited by 324
- PowerSeries.constantCoeffstatement and proof · cited by 126
- PowerSeries.orderstatement and proof · cited by 92
- PowerSeries.coeff_zero_eq_constantCoeffproof · cited by 41
- Order.one_le_iff_posproof · cited by 27
- PowerSeries.coeff_of_lt_orderproof · cited by 14
Cited by2
Results whose statement or proof uses this declaration.
- PowerSeries.order_ne_zero_iff_constCoeff_eq_zeroproof · cited by 1
- PowerSeries.le_order_pow_of_constantCoeff_eq_zeroproof · cited by 1