Theorems · Theorem · several complex variables

FormalMultilinearSeries.changeOrigin_finite_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] {x : E}
  (p : FormalMultilinearSeries 𝕜 E F) {n : ℕ}, (∀ (m : ℕ), n ≤ m → p m = 0) → ∀ {k : ℕ}, n ≤ k → p.changeOrigin x k = 0

If p is a formal multilinear series such that p m = 0 for n ≤ m, then p.changeOrigin x k = 0 for n ≤ k.

Defined in

Mathlib.Analysis.Analytic.CPolynomialDef

Cited by

2 results in Mathlib

Foundations

Depth 183 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace