Theorems · Theorem · commutative algebra
MvPowerSeries.le_order_pow
∀ {σ : Type u_1} {R : Type u_2} [inst : Semiring R] {f : MvPowerSeries σ R} (n : ℕ), n • f.order ≤ (f ^ n).order- Defined in
- Mathlib.RingTheory.MvPowerSeries.Order
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 93 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.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- ENatstatement · cited by 4,985
- MvPowerSeriesstatement and proof · cited by 659
- MvPowerSeries.orderstatement · cited by 45
- MvPowerSeries.le_weightedOrder_powproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- MvPowerSeries.WithPiTopology.summable_pow_of_constantCoeff_eq_zeroproof · cited by 3
- MvPowerSeries.le_order_pow_of_constantCoeff_eq_zeroproof · cited by 1