Theorems · Theorem · real analysis
ContDiffWithinAt.differentiableWithinAt_iteratedDerivWithin
∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {F : Type u_2} [inst_1 : NormedAddCommGroup F]
[inst_2 : NormedSpace 𝕜 F] {f : 𝕜 → F} {s : Set 𝕜} {x : 𝕜} {n : WithTop ℕ∞} {m : ℕ},
ContDiffWithinAt 𝕜 n f s x →
↑m < n → UniqueDiffOn 𝕜 (insert x s) → DifferentiableWithinAt 𝕜 (iteratedDerivWithin m f s) s x- Cited by
- 1 results in Mathlib
- Foundations
- Depth 187 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- ENatstatement and proof · cited by 4,985
- WithTopstatement and proof · cited by 3,754
- DifferentiableWithinAtstatement and proof · cited by 453
- LinearIsometryEquiv.symmproof · cited by 287
- ContDiffWithinAtstatement and proof · cited by 283
- UniqueDiffOnstatement and proof · cited by 215
- iteratedDerivWithinstatement · cited by 122
- ContinuousMultilinearMap.piFieldEquivproof · cited by 15
Cited by1
Results whose statement or proof uses this declaration.
- ContDiffOn.differentiableOn_iteratedDerivWithinproof · cited by 6