Theorems · Theorem · several complex variables
analyticAt_congr
∀ {𝕜 : Type u_1} {E : Type u_2} {F : Type u_3} [inst : NontriviallyNormedField 𝕜] [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F] {f g : E → F} {x : E},
f =ᶠ[nhds x] g → (AnalyticAt 𝕜 f x ↔ AnalyticAt 𝕜 g x)- Defined in
- Mathlib.Analysis.Analytic.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 169 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- nhdsstatement and proof · cited by 5,554
- Filter.EventuallyEqstatement and proof · cited by 1,912
- Filter.EventuallyEq.symmproof · cited by 408
- AnalyticAtstatement and proof · cited by 321
- AnalyticAt.congrproof · cited by 12
Cited by5
Results whose statement or proof uses this declaration.
- analyticOrderAt_eq_topproof · cited by 12
- meromorphicNFAt_toMeromorphicNFAtproof · cited by 5
- meromorphicNFAt_iff_analyticAt_orproof · cited by 3
- analyticAt_iff_analytic_fun_smulproof · cited by 1
- HarmonicAt.analyticAtproof · cited by 0