Theorems · Theorem · complex analysis
AnalyticAt.meromorphicAt
∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_3} [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] {f : 𝕜 → E} {x : 𝕜}, AnalyticAt 𝕜 f x → MeromorphicAt f x- Defined in
- Mathlib.Analysis.Meromorphic.Basic
- Cited by
- 22 results in Mathlib
- Foundations
- Depth 167 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- one_smulproof · cited by 1,374
- pow_zeroproof · cited by 1,094
- AnalyticAtstatement and proof · cited by 321
- MeromorphicAtstatement · cited by 160
Cited by22
Results whose statement or proof uses this declaration.
- MeromorphicAt.constproof · cited by 36
- MeromorphicAt.idproof · cited by 18
- AnalyticOnNhd.meromorphicOnproof · cited by 13
- AnalyticAt.meromorphicTrailingCoeffAt_of_ne_zero_of_eq_nhdsNEproof · cited by 11
- AnalyticAt.meromorphicOrderAt_eqproof · cited by 9
- MeromorphicNFAt.meromorphicAtproof · cited by 7
- MeromorphicAt.derivproof · cited by 6
- MeromorphicAt.sumproof · cited by 4
- AnalyticAt.meromorphicTrailingCoeffAt_of_eq_nhdsNEproof · cited by 4
- meromorphicNFAt_iff_analyticAt_orproof · cited by 3
- meromorphicOrderAt_addproof · cited by 2
- MeromorphicOn.negPart_divisor_add_of_analyticNhdOn_rightproof · cited by 2