Theorems · Theorem · several complex variables

HasFPowerSeriesWithinAt.const_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] {f : E → F}
  {pf : FormalMultilinearSeries 𝕜 E F} {s : Set E} {x : E} {R : Type u_9} [inst_5 : NormedRing R] [inst_6 : Module R F]
  [inst_7 : IsBoundedSMul R F] [inst_8 : SMulCommClass 𝕜 R F] {c : R},
  HasFPowerSeriesWithinAt f pf s x → HasFPowerSeriesWithinAt (c • f) (c • pf) s x

Defined in

Mathlib.Analysis.Analytic.Constructions

Cited by

1 results in Mathlib

Foundations

Depth 172 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceNormedRingModuleIsBoundedSMulSMulCommClass