Theorems · Theorem · commutative algebra
MvPowerSeries.le_order_prod
∀ {σ : Type u_1} {R : Type u_3} [inst : CommSemiring R] {ι : Type u_4} (f : ι → MvPowerSeries σ R) (s : Finset ι),
∑ i ∈ s, (f i).order ≤ (∏ i ∈ s, f i).order- Defined in
- Mathlib.RingTheory.MvPowerSeries.Order
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 96 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.
Cites8
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 · cited by 5,195
- ENatstatement · cited by 4,985
- Finset.prodstatement · cited by 2,356
- MvPowerSeriesstatement and proof · cited by 659
- MvPowerSeries.orderstatement · cited by 45
- MvPowerSeries.le_weightedOrder_prodproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- MvPowerSeries.truncTotal_subst_eq_truncTotal_subst_sumproof · cited by 2