Theorems · Theorem · several complex variables

HasFPowerSeriesAt.restrictScalars

∀ {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] {𝕜' : Type u_9}
  [inst_5 : NontriviallyNormedField 𝕜'] [inst_6 : NormedAlgebra 𝕜 𝕜'] [inst_7 : NormedSpace 𝕜' E]
  [inst_8 : IsScalarTower 𝕜 𝕜' E] [inst_9 : NormedSpace 𝕜' F] [inst_10 : IsScalarTower 𝕜 𝕜' F] {f : E → F}
  {p : FormalMultilinearSeries 𝕜' E F} {x : E},
  HasFPowerSeriesAt f p x → HasFPowerSeriesAt f (FormalMultilinearSeries.restrictScalars 𝕜 p) x

Defined in

Mathlib.Analysis.Analytic.Constructions

Cited by

1 results in Mathlib

Foundations

Depth 175 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceNontriviallyNormedFieldNormedAlgebraNormedSpaceIsScalarTowerNormedSpaceIsScalarTower