Theorems · Theorem · commutative algebra
PowerSeries.order_mul_ge
∀ {R : Type u_1} [inst : Semiring R] (φ ψ : PowerSeries R), φ.order + ψ.order ≤ (φ * ψ).orderAlias of PowerSeries.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.PowerSeries.Order
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 90 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 · cited by 13,802
- ENatstatement · cited by 4,985
- PowerSeriesstatement · cited by 797
- PowerSeries.orderstatement · cited by 92
- PowerSeries.le_order_mulproof · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- PowerSeries.order_zero_of_unitproof · cited by 2
- PowerSeries.HasSubst.eventually_coeff_pow_eq_zeroproof · cited by 1