Theorems · Theorem · several complex variables

AnalyticAt.fun_smul

∀ {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] {A : Type u_7}
  [inst_5 : NormedRing A] [inst_6 : NormedAlgebra 𝕜 A] [inst_7 : Module A F] [IsBoundedSMul A F] [IsScalarTower 𝕜 A F]
  {f : E → A} {g : E → F} {z : E}, AnalyticAt 𝕜 f z → AnalyticAt 𝕜 g z → AnalyticAt 𝕜 (fun i => f i • g i) z

Eta-expanded form of AnalyticAt.smul Scalar multiplication of one analytic function by another.

Defined in

Mathlib.Analysis.Analytic.Constructions

Cited by

10 results in Mathlib

Foundations

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

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceNormedRingNormedAlgebraModuleIsBoundedSMulIsScalarTower