Theorems · Theorem · commutative algebra

MvPowerSeries.coeff_subst_finite

∀ {σ : Type u_1} {R : Type u_3} [inst : CommRing R] {τ : Type u_4} {S : Type u_5} [inst_1 : CommRing S]
  [inst_2 : Algebra R S] {a : σ → MvPowerSeries τ S},
  MvPowerSeries.HasSubst a →
    ∀ (f : MvPowerSeries σ R) (e : τ →₀ ℕ),
      Function.HasFiniteSupport fun d => (MvPowerSeries.coeff d) f • (MvPowerSeries.coeff e) (d.prod fun s e => a s ^ e)

Defined in

Mathlib.RingTheory.MvPowerSeries.Substitution

Cited by

6 results in Mathlib

Foundations

Depth 105 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebra