Theorems · Theorem · complex analysis
meromorphicTrailingCoeffAt_congr_nhdsNE
∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] {x : 𝕜} {f₁ f₂ : 𝕜 → E},
f₁ =ᶠ[nhdsWithin x {x}ᶜ] f₂ → meromorphicTrailingCoeffAt f₁ x = meromorphicTrailingCoeffAt f₂ xIf two functions agree in a punctured neighborhood, then their trailing coefficients agree.
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 203 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites22
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
- Top.topproof · cited by 9,680
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- Compl.complstatement and proof · cited by 2,925
- nhdsWithinstatement and proof · cited by 1,912
- Filter.EventuallyEqstatement and proof · cited by 1,912
- Iff.notproof · cited by 489
- Filter.EventuallyEq.symmproof · cited by 408
- AnalyticAtproof · cited by 321
- meromorphicOrderAtproof · cited by 180
Cited by7
Results whose statement or proof uses this declaration.
- MeromorphicAt.meromorphicTrailingCoeffAt_add_eq_addproof · cited by 2
- MeromorphicAt.meromorphicTrailingCoeffAt_add_eq_left_of_ltproof · cited by 2
- MeromorphicOn.log_norm_meromorphicTrailingCoeffAt_extract_zeros_polesproof · cited by 1
- Complex.ECanonicalDecomp.eq_smul_meromorphicTrailingCoeffAtproof · cited by 1
- meromorphicTrailingCoeffAt_invproof · cited by 1
- MeromorphicAt.meromorphicTrailingCoeffAt_compproof · cited by 1
- MeromorphicOn.meromorphicTrailingCoeffAt_extract_zeros_polesproof · cited by 0