Theorems · Theorem · commutative algebra

MvPowerSeries.subst_tsum

∀ {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} {x : ℕ → MvPowerSeries σ R} [inst_3 : UniformSpace R]
  [DiscreteUniformity R] [inst_5 : UniformSpace S] [DiscreteUniformity S],
  Summable x →
    MvPowerSeries.HasSubst a → MvPowerSeries.subst a (∑' (i : ℕ), x i) = ∑' (i : ℕ), MvPowerSeries.subst a (x i)

Defined in

Mathlib.RingTheory.MvPowerSeries.Substitution

Cited by

0 results in Mathlib

Foundations

Depth 108 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebraUniformSpaceDiscreteUniformityUniformSpaceDiscreteUniformity