Theorems · Theorem · global analysis
AnalyticAt.deriv
∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {F : Type v} [inst_1 : NormedAddCommGroup F]
[inst_2 : NormedSpace 𝕜 F] {f : 𝕜 → F} {x : 𝕜} [CompleteSpace F], AnalyticAt 𝕜 f x → AnalyticAt 𝕜 (deriv f) x- Cited by
- 10 results in Mathlib
- Foundations
- Depth 193 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realproof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- CompleteSpacestatement and proof · cited by 2,532
- Metric.ballproof · cited by 735
- derivstatement · cited by 676
- AnalyticAtstatement and proof · cited by 321
- AnalyticOnNhdproof · cited by 206
- dist_selfproof · cited by 116
- AnalyticOnNhd.derivproof · cited by 3
- AnalyticAt.exists_ball_analyticOnNhdproof · cited by 2
Cited by10
Results whose statement or proof uses this declaration.
- MeromorphicAt.derivproof · cited by 6
- natCast_le_analyticOrderAt_iff_iteratedDeriv_eq_zeroproof · cited by 2
- analyticOrderAt_deriv_ge_iffproof · cited by 2
- meromorphicOrderAt_deriv_eq_sub_oneproof · cited by 2
- AnalyticAt.analyticOrderAt_deriv_add_oneproof · cited by 2
- AnalyticAt.iterated_derivproof · cited by 1
- meromorphicOrderAt_logDeriv_nonnegproof · cited by 0
- analyticOrderAt_eq_nat_iff_iteratedDeriv_eq_zeroproof · cited by 0
- iteratedDeriv_mul_pow_sub_of_analyticproof · cited by 0
- AnalyticAt.tendsto_mul_logDeriv_simple_zeroproof · cited by 0