Theorems · Theorem · complex analysis
toMeromorphicNFAt_eq_self
∀ {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}, toMeromorphicNFAt f x = f ↔ MeromorphicNFAt f xIf f has normal form at x, then f equals f.toNF.
- Defined in
- Mathlib.Analysis.Meromorphic.NormalForm
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 202 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites35
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
- nhdsproof · cited by 5,554
- WithTopproof · cited by 3,754
- Filter.Eventuallyproof · cited by 3,134
- Compl.complproof · cited by 2,925
- nhdsWithinproof · cited by 1,912
- Filter.EventuallyEqproof · cited by 1,912
- one_smulproof · cited by 1,374
- WithTop.someproof · cited by 1,128
- sub_selfproof · cited by 996
Cited by4
Results whose statement or proof uses this declaration.
- MeromorphicOn.extract_zeros_polesproof · cited by 4
- MeromorphicOn.toMeromorphicNFOn_eq_self_on_nhdsNEproof · cited by 3
- toMeromorphicNFOn_eqOn_codiscreteproof · cited by 1
- toMeromorphicNFOn_eq_selfproof · cited by 0