Theorems · Theorem · real analysis

iteratedFDerivWithin_one_apply

∀ {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] {s : Set E}
  {f : E → F} {x : E},
  UniqueDiffWithinAt 𝕜 s x → ∀ (m : Fin 1 → E), (iteratedFDerivWithin 𝕜 1 f s x) m = (fderivWithin 𝕜 f s x) (m 0)

Defined in

Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries

Cited by

3 results in Mathlib

Foundations

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

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace