Theorems · Theorem · real analysis

HasFTaylorSeriesUpTo.fderiv

∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {E : Type uE} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {F : Type uF} [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F] {n : WithTop ℕ∞}
  {f : E → F} {p : E → FormalMultilinearSeries 𝕜 E F},
  HasFTaylorSeriesUpTo n f p → ∀ (m : ℕ), ↑m < n → ∀ (x : E), HasFDerivAt (fun y => p y m) (p x m.succ).curryLeft x

Defined in

Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries

Cited by

2 results in Mathlib

Foundations

Depth 173 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace