Theorems · Theorem · complex analysis
AnalyticAt.analyticOrderAt_sub_eq_one_of_deriv_ne_zero
∀ {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 → deriv f x ≠ 0 → analyticOrderAt (fun x_1 => f x_1 - f x) x = 1- Defined in
- Mathlib.Analysis.Analytic.Order
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 197 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites34
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
- Top.topproof · cited by 9,680
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- nhdsproof · cited by 5,554
- ENatstatement · cited by 4,985
- Filter.Eventuallyproof · cited by 3,134
- add_zeroproof · cited by 2,707
- Nat.cast_oneproof · cited by 2,501
- MulZeroClass.mul_zeroproof · cited by 2,091
- MulZeroClass.zero_mulproof · cited by 1,625
- one_smulproof · cited by 1,374
Cited by3
Results whose statement or proof uses this declaration.
- meromorphicOrderAt_comp_of_deriv_ne_zeroproof · cited by 2
- analyticOrderAt_comp_of_deriv_ne_zeroproof · cited by 0
- AnalyticAt.analyticOrderAt_eq_one_of_zero_deriv_ne_zeroproof · cited by 0