Theorems · Theorem · real analysis

ContDiffWithinAt.derivWithin

∀ {𝕜 : Type u_1} {F : Type u_2} [inst : NontriviallyNormedField 𝕜] [inst_1 : NormedAddCommGroup F]
  [inst_2 : NormedSpace 𝕜 F] {m n : WithTop ℕ∞} {f : 𝕜 → F} {s : Set 𝕜} {x : 𝕜},
  ContDiffWithinAt 𝕜 n f s x → UniqueDiffOn 𝕜 s → m + 1 ≤ n → x ∈ s → ContDiffWithinAt 𝕜 m (derivWithin f s) s x

Defined in

Mathlib.Analysis.Calculus.ContDiff.Deriv

Cited by

2 results in Mathlib

Foundations

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

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpace