Theorems · Theorem · complex analysis
MeromorphicAt.eqOn_compl_singleton_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 → Set.EqOn f (toMeromorphicNFAt f x) {x}ᶜConversion to normal form at x changes the value only at x.
- Defined in
- Mathlib.Analysis.Meromorphic.NormalForm
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 199 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- Compl.complstatement and proof · cited by 2,925
- Set.EqOnstatement · cited by 603
- Function.update_of_neproof · cited by 198
- meromorphicOrderAtproof · cited by 180
- MeromorphicAtstatement and proof · cited by 160
- Function.update_congrproof · cited by 22
- toMeromorphicNFAtstatement · cited by 15
Cited by2
Results whose statement or proof uses this declaration.
- MeromorphicAt.eq_nhdsNE_toMeromorphicNFAtproof · cited by 5
- toMeromorphicNFAt_eq_selfproof · cited by 4