Theorems · Theorem · real analysis
ContDiffAt.hasStrictDerivAt
∀ {n : WithTop ℕ∞} {𝕂 : Type u_1} [inst : RCLike 𝕂] {F' : Type u_3} [inst_1 : NormedAddCommGroup F']
[inst_2 : NormedSpace 𝕂 F'] {f : 𝕂 → F'} {x : 𝕂}, ContDiffAt 𝕂 n f x → n ≠ 0 → HasStrictDerivAt f (deriv f x) xIf a function is C^n with 1 ≤ n around a point, then the derivative of f at this point
is also a strict derivative.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 197 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- ENatstatement and proof · cited by 4,985
- WithTopstatement and proof · cited by 3,754
- RCLikestatement and proof · cited by 2,829
- derivstatement · cited by 676
- ContDiffAtstatement and proof · cited by 262
- HasStrictDerivAtstatement · cited by 163
- HasStrictFDerivAt.hasStrictDerivAtproof · cited by 18
- ContDiffAt.hasStrictFDerivAtproof · cited by 11
Cited by1
Results whose statement or proof uses this declaration.
- ContDiff.hasStrictDerivAtproof · cited by 0