Theorems · Theorem · real analysis

ContDiffWithinAt.fderivWithin_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∞},
  ContDiffWithinAt 𝕜 n f s x₀ → UniqueDiffOn 𝕜 s → m + 1 ≤ n → x₀ ∈ s → ContDiffWithinAt 𝕜 m (fderivWithin 𝕜 f s) s x₀

fderivWithin 𝕜 f s is smooth at x₀ within s.

Defined in

Mathlib.Analysis.Calculus.ContDiff.Comp

Cited by

11 results in Mathlib

Foundations

Depth 205 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace