Theorems · Theorem · real analysis

ContDiffWithinAt.iteratedFDerivWithin_right

∀ {𝕜 : Type u_1} {E : Type u_2} {F : Type u_3} [inst : NontriviallyNormedField 𝕜] [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F] {s : Set E} {f : E → F} {x₀ : E}
  {m n : WithTop ℕ∞} {i : ℕ},
  ContDiffWithinAt 𝕜 n f s x₀ →
    UniqueDiffOn 𝕜 s → m + ↑i ≤ n → x₀ ∈ s → ContDiffWithinAt 𝕜 m (iteratedFDerivWithin 𝕜 i f s) s x₀

Defined in

Mathlib.Analysis.Calculus.ContDiff.Comp

Cited by

2 results in Mathlib

Foundations

Depth 206 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace