Theorems · Theorem · commutative algebra
MvPowerSeries.eq_zero_iff_forall_coeff_zero
∀ {σ : Type u_1} {R : Type u_2} [inst : Semiring R] {f : MvPowerSeries σ R},
f = 0 ↔ ∀ (d : σ →₀ ℕ), (MvPowerSeries.coeff d) f = 0- Defined in
- Mathlib.RingTheory.MvPowerSeries.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 31 from the axioms · uses propext, Quot.sound
- Assumes
- Semiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- RingHom.idstatement · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- LinearMapstatement · cited by 10,215
- Finsuppstatement · cited by 5,255
- MvPowerSeriesstatement and proof · cited by 659
- MvPowerSeries.coeffstatement · cited by 273
- MvPowerSeries.ext_iffproof · cited by 5
Cited by1
Results whose statement or proof uses this declaration.
- MvPowerSeries.eq_zero_iff_forall_coeff_eq_zero_andproof · cited by 0