Theorems · Theorem · commutative algebra
PowerSeries.le_order_prod
∀ {R : Type u_2} [inst : CommSemiring R] {ι : Type u_3} (φ : ι → PowerSeries R) (s : Finset ι),
∑ i ∈ s, (φ i).order ≤ (∏ i ∈ s, φ i).order- Defined in
- Mathlib.RingTheory.PowerSeries.Order
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement and proof · cited by 13,712
- CommSemiringstatement and proof · cited by 10,911
- Finset.sumstatement and proof · cited by 5,195
- ENatstatement and proof · cited by 4,985
- Finset.prodstatement and proof · cited by 2,356
- le_reflproof · cited by 2,061
- PowerSeriesstatement and proof · cited by 797
- add_le_addproof · cited by 666
- le_imp_le_of_le_of_leproof · cited by 576
- Finset.consproof · cited by 221
- PowerSeries.orderstatement and proof · cited by 92
- Finset.cons_inductionproof · cited by 85
Cited by1
Results whose statement or proof uses this declaration.
- PowerSeries.WithPiTopology.summable_prod_of_tendsto_order_atTop_nhds_topproof · cited by 1