Theorems · Theorem · commutative algebra
MvPowerSeries.coeff_of_lt_order
∀ {σ : Type u_1} {R : Type u_2} [inst : Semiring R] {f : MvPowerSeries σ R} {d : σ →₀ ℕ},
↑(Finsupp.degree d) < f.order → (MvPowerSeries.coeff d) f = 0The nth coefficient of a formal power series is 0 if n is strictly
smaller than the order of the power series.
- Defined in
- Mathlib.RingTheory.MvPowerSeries.Order
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 85 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.
Cites13
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
- Finsuppstatement and proof · cited by 5,255
- ENatstatement · cited by 4,985
- AddMonoidHomstatement and proof · cited by 3,230
- MvPowerSeriesstatement and proof · cited by 659
- MvPowerSeries.coeffstatement · cited by 273
- Finsupp.degreestatement and proof · cited by 94
- MvPowerSeries.orderstatement and proof · cited by 45
- Finsupp.degree_eq_weight_oneproof · cited by 26
Cited by5
Results whose statement or proof uses this declaration.
- PowerSeries.order_eq_orderproof · cited by 4
- MvPowerSeries.one_le_order_iff_constCoeff_eq_zeroproof · cited by 2
- MvPowerSeries.truncTotal_subst_eq_truncTotal_subst_sumproof · cited by 2
- MvPowerSeries.order_expandproof · cited by 1
- MvPowerSeries.order_toSubringproof · cited by 0