Theorems · Theorem · commutative algebra
PowerSeries.le_order_mul
∀ {R : Type u_1} [inst : Semiring R] (φ ψ : PowerSeries R), φ.order + ψ.order ≤ (φ * ψ).orderThe 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
- 5 results in Mathlib
- Foundations
- Depth 89 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.
Cites18
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
- ENatstatement and proof · cited by 4,985
- MulZeroClass.mul_zeroproof · cited by 2,091
- MulZeroClass.zero_mulproof · cited by 1,625
- PowerSeriesstatement and proof · cited by 797
- add_le_addproof · cited by 666
- Nat.cast_addproof · cited by 586
- lt_of_lt_of_leproof · cited by 438
- PowerSeries.coeffproof · cited by 324
- Finset.HasAntidiagonal.antidiagonalproof · cited by 218
- ne_of_ltproof · cited by 203
Cited by5
Results whose statement or proof uses this declaration.
- PowerSeries.order_mulproof · cited by 2
- PowerSeries.order_mul_geproof · cited by 2
- PowerSeries.le_order_prodproof · cited by 1
- PowerSeries.le_order_powproof · cited by 1
- Nat.Partition.tendsto_order_genFun_term_atTop_nhds_topproof · cited by 1