Theorems · Theorem · commutative algebra
MvPowerSeries.order_mul_ge
∀ {σ : Type u_1} {R : Type u_2} [inst : Semiring R] {f g : MvPowerSeries σ R}, f.order + g.order ≤ (f * g).orderAlias of MvPowerSeries.le_order_mul.
The order 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 90 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Semiring
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Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement · cited by 13,802
- ENatstatement · cited by 4,985
- MvPowerSeriesstatement · cited by 659
- MvPowerSeries.orderstatement · cited by 45
- MvPowerSeries.le_order_mulproof · cited by 1
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