Theorems · Theorem · complex analysis
analyticOrderAt_of_not_analyticAt
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : NontriviallyNormedField 𝕜] [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] {f : 𝕜 → E} {z₀ : 𝕜}, ¬AnalyticAt 𝕜 f z₀ → analyticOrderAt f z₀ = 0- Defined in
- Mathlib.Analysis.Analytic.Order
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 195 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- ENatstatement · cited by 4,985
- AnalyticAtstatement and proof · cited by 321
- analyticOrderAtstatement · cited by 69
Cited by8
Results whose statement or proof uses this declaration.
- analyticOrderAt_eq_zeroproof · cited by 3
- le_analyticOrderAt_addproof · cited by 2
- analyticOrderAt_congrproof · cited by 1
- analyticOrderAt_negproof · cited by 1
- analyticOrderNatAt_of_not_analyticAtproof · cited by 0
- analyticOrderAt_comp_of_deriv_ne_zeroproof · cited by 0
- apply_eq_zero_of_analyticOrderAt_ne_zeroproof · cited by 0
- apply_eq_zero_of_analyticOrderNatAt_ne_zeroproof · cited by 0