Theorems · Theorem · real analysis
ContDiffAt.differentiableAt_iteratedFDeriv
∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {E : Type uE} [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] {F : Type uF} [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F] {f : E → F}
{n : WithTop ℕ∞} {m : ℕ} {x : E}, ContDiffAt 𝕜 n f x → ↑m < n → DifferentiableAt 𝕜 (iteratedFDeriv 𝕜 m f) x- Defined in
- Mathlib.Analysis.Calculus.ContDiff.Defs
- Cited by
- 4 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.
Cites21
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- TopologicalSpaceproof · cited by 24,529
- Moduleproof · cited by 20,661
- NormedAddCommGroupstatement and proof · cited by 15,752
- AddCommGroupproof · cited by 12,871
- NormedSpacestatement and proof · cited by 12,499
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- ENatstatement and proof · cited by 4,985
- Set.univproof · cited by 3,945
- WithTopstatement and proof · cited by 3,754
- ContinuousMultilinearMapstatement and proof · cited by 1,016
- DifferentiableAtstatement · cited by 617
Cited by4
Results whose statement or proof uses this declaration.
- ContDiffAt.contDiffPointwiseHolderAtproof · cited by 6
- ContDiffAt.deriv_fderiv_add_smulproof · cited by 1
- iteratedFDeriv_comp_const_smulproof · cited by 1
- map_add_eq_sum_add_integral_iteratedFDerivproof · cited by 0