Theorems · Theorem · complex analysis
AnalyticAt.analyticOrderAt_deriv_add_one
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : NontriviallyNormedField 𝕜] [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] {f : 𝕜 → E} {x : 𝕜},
AnalyticAt 𝕜 f x →
∀ [CompleteSpace E] [CharZero 𝕜], analyticOrderAt (deriv f) x + 1 = analyticOrderAt (fun x_1 => f x_1 - f x) x- Defined in
- Mathlib.Analysis.Analytic.Order
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 201 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites67
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Moduleproof · cited by 20,661
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- AddCommMonoidproof · cited by 12,281
- Top.topproof · cited by 9,680
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- nhdsproof · cited by 5,554
- ENatstatement and proof · cited by 4,985
- mul_oneproof · cited by 3,885
- Filter.Eventuallyproof · cited by 3,134
- CompleteSpacestatement and proof · cited by 2,532
Cited by2
Results whose statement or proof uses this declaration.
- natCast_le_analyticOrderAt_iff_iteratedDeriv_eq_zeroproof · cited by 2
- analyticOrderAt_deriv_of_posproof · cited by 2