Theorems · Theorem · commutative algebra
MvPowerSeries.le_weightedOrder_pow
∀ {σ : Type u_1} {R : Type u_2} [inst : Semiring R] (w : σ → ℕ) {f : MvPowerSeries σ R} (n : ℕ),
n • MvPowerSeries.weightedOrder w f ≤ MvPowerSeries.weightedOrder w (f ^ n)- Defined in
- Mathlib.RingTheory.MvPowerSeries.Order
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 92 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.
Cites12
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 and proof · cited by 4,985
- le_reflproof · cited by 2,061
- pow_zeroproof · cited by 1,094
- add_le_addproof · cited by 666
- MvPowerSeriesstatement and proof · cited by 659
- le_imp_le_of_le_of_leproof · cited by 576
- pow_succproof · cited by 374
- zero_nsmulproof · cited by 137
- succ_nsmulproof · cited by 65
- MvPowerSeries.weightedOrderstatement and proof · cited by 37
- MvPowerSeries.le_weightedOrder_mulproof · cited by 7
Cited by2
Results whose statement or proof uses this declaration.
- MvPowerSeries.le_weightedOrder_substproof · cited by 3
- MvPowerSeries.le_order_powproof · cited by 2