Theorems · Theorem · complex analysis

MeromorphicNFAt.smul_analytic

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {f : 𝕜 → E} {g : 𝕜 → 𝕜} {x : 𝕜},
  MeromorphicNFAt f x → AnalyticAt 𝕜 g x → g x ≠ 0 → MeromorphicNFAt (g • f) x

Helper lemma for meromorphicNFAt_iff_meromorphicNFAt_of_smul_analytic: if f is meromorphic in normal form at x and g is analytic without zero at x, then g • f is meromorphic in normal form at x.

Defined in

Mathlib.Analysis.Meromorphic.NormalForm

Cited by

2 results in Mathlib

Foundations

Depth 188 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpace