Theorems · Theorem · commutative algebra
MvPowerSeries.le_weightedOrder_prod
∀ {σ : Type u_1} {R : Type u_3} [inst : CommSemiring R] {ι : Type u_4} (w : σ → ℕ) (f : ι → MvPowerSeries σ R)
(s : Finset ι), ∑ i ∈ s, MvPowerSeries.weightedOrder w (f i) ≤ MvPowerSeries.weightedOrder w (∏ i ∈ s, f i)- Defined in
- Mathlib.RingTheory.MvPowerSeries.Order
- Cited by
- 3 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
- add_le_addproof · cited by 666
- MvPowerSeriesstatement and proof · cited by 659
- le_imp_le_of_le_of_leproof · cited by 576
- Finset.consproof · cited by 221
- Finset.cons_inductionproof · cited by 85
- Finset.sum_consproof · cited by 84
Cited by3
Results whose statement or proof uses this declaration.
- MvPowerSeries.le_weightedOrder_substproof · cited by 3
- MvPowerSeries.le_order_prodproof · cited by 1