Theorems · Theorem · several complex variables

FormalMultilinearSeries.changeOriginSeries_sum_eq_partialSum_of_finite

∀ {𝕜 : Type u_1} {E : Type u_2} {F : Type u_3} [inst : NontriviallyNormedField 𝕜] [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F]
  (p : FormalMultilinearSeries 𝕜 E F) {n : ℕ},
  (∀ (m : ℕ), n ≤ m → p m = 0) → ∀ (k : ℕ), (p.changeOriginSeries k).sum = (p.changeOriginSeries k).partialSum (n - k)

Defined in

Mathlib.Analysis.Analytic.CPolynomialDef

Cited by

1 results in Mathlib

Foundations

Depth 182 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace