Theorems · Theorem · complex analysis

MeromorphicAt.fun_smul

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_3} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {R : Type u_4} [inst_3 : NormedRing R] [inst_4 : Module R E] [IsBoundedSMul R E] {x : 𝕜}
  [inst_6 : NormedAlgebra 𝕜 R] [IsScalarTower 𝕜 R E] {f : 𝕜 → R} {g : 𝕜 → E},
  MeromorphicAt f x → MeromorphicAt g x → MeromorphicAt (fun i => f i • g i) x

Eta-expanded form of MeromorphicAt.smul

Defined in

Mathlib.Analysis.Meromorphic.Basic

Cited by

3 results in Mathlib

Foundations

Depth 189 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedRingModuleIsBoundedSMulNormedAlgebraIsScalarTower