Theorems · Theorem · global analysis
AnalyticAt.hasStrictDerivAt
∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {F : Type v} [inst_1 : NormedAddCommGroup F]
[inst_2 : NormedSpace 𝕜 F] {f : 𝕜 → F} {x : 𝕜}, AnalyticAt 𝕜 f x → HasStrictDerivAt f (deriv f x) x- Cited by
- 3 results in Mathlib
- Foundations
- Depth 185 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- derivstatement · cited by 676
- AnalyticAtstatement and proof · cited by 321
- HasStrictFDerivAtproof · cited by 261
- HasStrictDerivAtstatement · cited by 163
- toSpanSingleton_derivproof · cited by 4
- AnalyticAt.hasStrictFDerivAtproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- meromorphicAt_comp_iff_of_deriv_ne_zeroproof · cited by 2
- AnalyticAt.analyticAt_localInversestatement and proof · cited by 2
- analyticAt_comp_iff_of_deriv_ne_zeroproof · cited by 2