Theorems · Theorem · real analysis
iteratedDerivWithin_eq_iteratedDeriv
∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {F : Type u_2} [inst_1 : NormedAddCommGroup F]
[inst_2 : NormedSpace 𝕜 F] {n : ℕ} {f : 𝕜 → F} {s : Set 𝕜} {x : 𝕜},
UniqueDiffOn 𝕜 s → ContDiffAt 𝕜 (↑n) f x → x ∈ s → iteratedDerivWithin n f s x = iteratedDeriv n f x- Cited by
- 9 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.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- 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 · cited by 4,985
- WithTopstatement · cited by 3,754
- ContinuousMultilinearMapproof · cited by 1,016
- ContDiffAtstatement and proof · cited by 262
- UniqueDiffOnstatement and proof · cited by 215
- iteratedFDerivproof · cited by 211
- iteratedDerivstatement and proof · cited by 188
Cited by9
Results whose statement or proof uses this declaration.
- Function.hasTemperateGrowth_one_add_norm_sq_rpowproof · cited by 9
- Real.iteratedDerivWithin_sinh_Iccproof · cited by 0
- Real.iteratedDerivWithin_sinh_Iooproof · cited by 0
- Real.iteratedDerivWithin_cos_Iccproof · cited by 0
- Real.iteratedDerivWithin_cos_Iooproof · cited by 0
- Real.iteratedDerivWithin_cosh_Iccproof · cited by 0
- Real.iteratedDerivWithin_cosh_Iooproof · cited by 0
- Real.iteratedDerivWithin_sin_Iccproof · cited by 0
- Real.iteratedDerivWithin_sin_Iooproof · cited by 0