Theorems · Theorem · real analysis
ContDiff.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}, ContDiff 𝕂 n f → n ≠ 0 → HasStrictDerivAt f (deriv f x) xIf a function is C^n with 1 ≤ n, then the derivative of f is also a strict derivative.
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- Foundations
- Depth 198 from the axioms · uses propext, Classical.choice, Quot.sound
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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
- ContDiffstatement and proof · cited by 352
- HasStrictDerivAtstatement · cited by 163
- ContDiff.contDiffAtproof · cited by 106
- ContDiffAt.hasStrictDerivAtproof · cited by 1
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