Theorems · Theorem · several complex variables

AnalyticAt.div_const

∀ {𝕜 : Type u_2} [inst : NontriviallyNormedField 𝕜] {E : Type u_3} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {𝕝 : Type u_8} [inst_3 : NormedDivisionRing 𝕝] [inst_4 : NormedAlgebra 𝕜 𝕝] {x : E}
  {f : E → 𝕝}, AnalyticAt 𝕜 f x → ∀ {c : 𝕝}, AnalyticAt 𝕜 (fun x => f x / c) x

Defined in

Mathlib.Analysis.Analytic.Constructions

Cited by

2 results in Mathlib

Foundations

Depth 174 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedDivisionRingNormedAlgebra