Theorems · Theorem · complex analysis
analyticOrderAt_deriv_of_pos
∀ {𝕜 : Type u_3} {E : Type u_4} [inst : NontriviallyNormedField 𝕜] [CharZero 𝕜] [inst_2 : NormedAddCommGroup E]
[inst_3 : NormedSpace 𝕜 E] [CompleteSpace E] {f : 𝕜 → E} {z₀ : 𝕜},
AnalyticAt 𝕜 f z₀ → ∀ {n : ℕ}, analyticOrderAt f z₀ = ↑n + 1 → analyticOrderAt (deriv f) z₀ = ↑n- Defined in
- Mathlib.Analysis.Analytic.Order
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 202 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
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
- nhdsproof · cited by 5,554
- ENatstatement · cited by 4,985
- Filter.Eventuallyproof · cited by 3,134
- CompleteSpacestatement and proof · cited by 2,532
- sub_selfproof · cited by 996
- sub_zeroproof · cited by 938
- CharZerostatement and proof · cited by 932
- zero_smulproof · cited by 716
- derivstatement and proof · cited by 676
Cited by2
Results whose statement or proof uses this declaration.
- analyticOrderAt_eq_nat_iff_iteratedDeriv_eq_zeroproof · cited by 0
- analyticOrderAt_iterated_derivproof · cited by 0