Theorems · Theorem · commutative algebra
MvPowerSeries.weightedHomogeneousComponent_of_weightedOrder
∀ {σ : Type u_1} {R : Type u_2} [inst : Semiring R] {w : σ → ℕ} {f : MvPowerSeries σ R} {p : ℕ},
↑p = MvPowerSeries.weightedOrder w f → (MvPowerSeries.weightedHomogeneousComponent w p) f ≠ 0- Defined in
- Mathlib.RingTheory.MvPowerSeries.Order
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 84 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.
Cites15
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
- Semiringstatement and proof · cited by 13,802
- LinearMapstatement · cited by 10,215
- Finsuppproof · cited by 5,255
- ENatstatement and proof · cited by 4,985
- MvPowerSeriesstatement and proof · cited by 659
- MvPowerSeries.coeffproof · cited by 273
- ENat.toNatproof · cited by 143
- Finsupp.weightproof · cited by 90
- MvPowerSeries.weightedOrderstatement and proof · cited by 37
- ENat.toNat_natCastproof · cited by 8
Cited by2
Results whose statement or proof uses this declaration.
- MvPowerSeries.weightedOrder_mulproof · cited by 2
- MvPowerSeries.homogeneousComponent_of_orderproof · cited by 0