Theorems · Theorem · complex analysis
HasFPowerSeriesAt.locally_ne_zero
∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] {p : FormalMultilinearSeries 𝕜 𝕜 E} {f : 𝕜 → E} {z₀ : 𝕜},
HasFPowerSeriesAt f p z₀ → p ≠ 0 → ∀ᶠ (z : 𝕜) in nhdsWithin z₀ {z₀}ᶜ, f z ≠ 0- Defined in
- Mathlib.Analysis.Analytic.IsolatedZeros
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 188 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites25
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- 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
- Filter.Eventuallystatement and proof · cited by 3,134
- Compl.complstatement and proof · cited by 2,925
- nhdsWithinstatement · cited by 1,912
- Filter.univ_mem'proof · cited by 1,672
- Filter.mp_memproof · cited by 1,537
- Nat.iterateproof · cited by 740
- ContinuousAtproof · cited by 697
Cited by1
Results whose statement or proof uses this declaration.
- AnalyticAt.eventually_eq_zero_or_eventually_ne_zeroproof · cited by 6