Theorems · Theorem · commutative algebra
MvPowerSeries.coeff_prod
∀ {σ : Type u_1} {R : Type u_3} [inst : CommSemiring R] {ι : Type u_4} [inst_1 : DecidableEq ι] [inst_2 : DecidableEq σ]
(f : ι → MvPowerSeries σ R) (d : σ →₀ ℕ) (s : Finset ι),
(MvPowerSeries.coeff d) (∏ j ∈ s, f j) = ∑ l ∈ s.finsuppAntidiag d, ∏ i ∈ s, (MvPowerSeries.coeff (l i)) (f i)Coefficients of a product of power series
- Defined in
- Mathlib.RingTheory.MvPowerSeries.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites41
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- RingHom.idstatement · cited by 18,349
- Finsetstatement and proof · cited by 13,712
- CommSemiringstatement and proof · cited by 10,911
- LinearMapstatement · cited by 10,215
- Finsuppstatement and proof · cited by 5,255
- Finset.sumstatement and proof · cited by 5,195
- mul_oneproof · cited by 3,885
- Nat.cast_oneproof · cited by 2,501
- Finset.prodstatement and proof · cited by 2,356
- Finset.cardproof · cited by 2,327
- Finset.sum_congrproof · cited by 2,323
Cited by3
Results whose statement or proof uses this declaration.
- PowerSeries.coeff_prodproof · cited by 2
- MvPowerSeries.truncTotal_subst_eq_truncTotal_subst_truncTotal_of_leproof · cited by 1
- MvPowerSeries.coeff_powproof · cited by 1