Theorems · Theorem · commutative algebra
PowerSeries.order_mul
∀ {R : Type u_1} [inst : Semiring R] [NoZeroDivisors R] (φ ψ : PowerSeries R), (φ * ψ).order = φ.order + ψ.orderThe order of the product of two formal power series over an integral domain is the sum of their orders.
- Defined in
- Mathlib.RingTheory.PowerSeries.Order
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringNoZeroDivisors
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites27
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Semiringstatement and proof · cited by 13,802
- Top.topproof · cited by 9,680
- ENatstatement and proof · cited by 4,985
- MulZeroClass.mul_zeroproof · cited by 2,091
- le_antisymmproof · cited by 2,068
- MulZeroClass.zero_mulproof · cited by 1,625
- PowerSeriesstatement and proof · cited by 797
- NoZeroDivisorsstatement and proof · cited by 545
- PowerSeries.coeffproof · cited by 324
- Finset.HasAntidiagonal.antidiagonalproof · cited by 218
- mul_ne_zeroproof · cited by 178
Cited by3
Results whose statement or proof uses this declaration.
- PowerSeries.orderHomproof · cited by 3
- ModularForm.sturm_bound_levelOne_natproof · cited by 1
- PowerSeries.divXPowOrder_mulproof · cited by 0