Theorems · Theorem · global analysis
AnalyticAt.differentiableAt
∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u} [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] {F : Type v} [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F] {f : E → F}
{x : E}, AnalyticAt 𝕜 f x → DifferentiableAt 𝕜 f x- Cited by
- 18 results in Mathlib
- Foundations
- Depth 184 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- DifferentiableAtstatement and proof · cited by 617
- FormalMultilinearSeriesproof · cited by 615
- AnalyticAtstatement and proof · cited by 321
- HasFPowerSeriesAtproof · cited by 94
- HasFPowerSeriesAt.differentiableAtproof · cited by 1
Cited by18
Results whose statement or proof uses this declaration.
- MeromorphicAt.derivproof · cited by 6
- AnalyticAt.differentiableWithinAtproof · cited by 5
- Complex.differentiableOn_compl_singleton_and_continuousAt_iffproof · cited by 4
- MeromorphicOn.logDeriv_prod_eventuallyEqproof · cited by 3
- ProbabilityTheory.differentiableAt_mgfproof · cited by 3
- AnalyticAt.analyticOrderAt_sub_eq_one_of_deriv_ne_zeroproof · cited by 3
- MeromorphicOn.logDeriv_zpow_eventuallyEqproof · cited by 2
- meromorphicOrderAt_deriv_eq_sub_oneproof · cited by 2
- AnalyticAt.analyticOrderAt_deriv_add_oneproof · cited by 2
- MeromorphicOn.logDeriv_mul_eventuallyEqproof · cited by 2
- AnalyticOnNhd.hasFTaylorSeriesUpToOnproof · cited by 1
- ProbabilityTheory.differentiableAt_iteratedDeriv_mgfproof · cited by 1