Theorems · Theorem · commutative algebra
PowerSeries.coeff_subst
∀ {R : Type u_2} [inst : CommRing R] {τ : Type u_3} {S : Type u_4} [inst_1 : CommRing S] [inst_2 : Algebra R S]
{a : MvPowerSeries τ S},
PowerSeries.HasSubst a →
∀ (f : PowerSeries R) (e : τ →₀ ℕ),
(MvPowerSeries.coeff e) (PowerSeries.subst a f) =
∑ᶠ (d : ℕ), (PowerSeries.coeff d) f • (MvPowerSeries.coeff e) (a ^ d)- Cited by
- 4 results in Mathlib
- Foundations
- Depth 109 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites27
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 and proof · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- Semiringproof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- LinearMapstatement and proof · cited by 10,215
- Finsuppstatement and proof · cited by 5,255
- Equiv.symmproof · cited by 3,681
- pow_zeroproof · cited by 1,094
- Finsupp.singleproof · cited by 943
- PowerSeriesstatement and proof · cited by 797
- MvPowerSeriesstatement and proof · cited by 659
Cited by4
Results whose statement or proof uses this declaration.
- PowerSeries.coeff_subst'proof · cited by 4
- PowerSeries.toMvPowerSeries_coeff_eq_zeroproof · cited by 1
- PowerSeries.coeff_subst_singleproof · cited by 1
- PowerSeries.constantCoeff_substproof · cited by 0