Theorems · Theorem · several complex variables

AnalyticAt.fun_add

∀ {𝕜 : Type u_2} [inst : NontriviallyNormedField 𝕜] {E : Type u_3} {F : Type u_4} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F] {f g : E → F} {x : E},
  AnalyticAt 𝕜 f x → AnalyticAt 𝕜 g x → AnalyticAt 𝕜 (fun i => f i + g i) x

Eta-expanded form of AnalyticAt.add

Defined in

Mathlib.Analysis.Analytic.Constructions

Cited by

9 results in Mathlib

Foundations

Depth 176 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace