Theorems · Theorem · commutative algebra
MvPowerSeries.weightedOrder_mul_ge
∀ {σ : Type u_1} {R : Type u_2} [inst : Semiring R] (w : σ → ℕ) {f g : MvPowerSeries σ R},
MvPowerSeries.weightedOrder w f + MvPowerSeries.weightedOrder w g ≤ MvPowerSeries.weightedOrder w (f * g)Alias of MvPowerSeries.le_weightedOrder_mul.
The weightedOrder of the product of two formal power series
is at least the sum of their orders.
- Defined in
- Mathlib.RingTheory.MvPowerSeries.Order
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 89 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Semiring
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Cites5
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- Semiringstatement · cited by 13,802
- ENatstatement · cited by 4,985
- MvPowerSeriesstatement · cited by 659
- MvPowerSeries.weightedOrderstatement · cited by 37
- MvPowerSeries.le_weightedOrder_mulproof · cited by 7
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