Theorems · Theorem · commutative algebra
MvPowerSeries.coeff_expand_of_not_dvd
∀ {σ : Type u_1} {R : Type u_3} [inst : CommRing R] (p : ℕ) (hp : p ≠ 0) (φ : MvPowerSeries σ R) {m : σ →₀ ℕ} {i : σ},
¬p ∣ m i → (MvPowerSeries.coeff m) ((MvPowerSeries.expand p hp) φ) = 0- Defined in
- Mathlib.RingTheory.MvPowerSeries.Expand
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 109 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites23
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
- RingHom.idstatement · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- Algebraproof · cited by 11,388
- LinearMapstatement · cited by 10,215
- Finsuppstatement and proof · cited by 5,255
- AlgHomstatement · cited by 3,236
- one_mulproof · cited by 2,841
- MulZeroClass.mul_zeroproof · cited by 2,091
- map_oneproof · cited by 861
- MvPowerSeriesstatement and proof · cited by 659
- MvPowerSeries.coeffstatement and proof · cited by 273
Cited by5
Results whose statement or proof uses this declaration.
- MvPowerSeries.trunc'_expandproof · cited by 2
- MvPowerSeries.expand_eq_expandproof · cited by 2
- MvPowerSeries.order_expandproof · cited by 1
- PowerSeries.coeff_expand_of_not_dvdproof · cited by 1
- MvPowerSeries.support_expand_subsetproof · cited by 1