Theorems · Theorem · real analysis
ContDiff.differentiable_deriv_two
∀ {𝕜 : Type u_1} {F : Type u_2} [inst : NontriviallyNormedField 𝕜] [inst_1 : NormedAddCommGroup F]
[inst_2 : NormedSpace 𝕜 F] {f : 𝕜 → F}, ContDiff 𝕜 2 f → Differentiable 𝕜 (deriv f)- Defined in
- Mathlib.Analysis.Calculus.ContDiff.Deriv
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 207 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.
- 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
- derivstatement · cited by 676
- ContDiffstatement and proof · cited by 352
- Differentiablestatement · cited by 298
- contDiff_idproof · cited by 40
- differentiable_constproof · cited by 14
- ContDiff.fun_compproof · cited by 10
- ContDiff.sndproof · cited by 7
Cited by1
Results whose statement or proof uses this declaration.
- Differentiable.derivproof · cited by 2