Theorems · Theorem · complex analysis
MeromorphicAt.meromorphicOrderAt_nonneg_iff_analyticAt_toMeromorphicNFAt
∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] {f : 𝕜 → E} {x : 𝕜},
MeromorphicAt f x → (0 ≤ meromorphicOrderAt f x ↔ AnalyticAt 𝕜 (toMeromorphicNFAt f x) x)- Defined in
- Mathlib.Analysis.Meromorphic.NormalForm
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 202 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites11
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
- WithTopstatement · cited by 3,754
- AnalyticAtstatement · cited by 321
- meromorphicOrderAtstatement and proof · cited by 180
- MeromorphicAtstatement and proof · cited by 160
- toMeromorphicNFAtstatement · cited by 15
- meromorphicNFAt_toMeromorphicNFAtproof · cited by 5
- MeromorphicNFAt.meromorphicOrderAt_nonneg_iff_analyticAtproof · cited by 5
- MeromorphicAt.meromorphicOrderAt_toMeromorphicNFAtproof · cited by 2
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