Theorems · Theorem · complex analysis
meromorphicAt_comp_iff_of_deriv_ne_zero
∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_3} [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] {x : 𝕜} [CompleteSpace 𝕜] [CharZero 𝕜] {f : 𝕜 → E} {g : 𝕜 → 𝕜},
AnalyticAt 𝕜 g x → deriv g x ≠ 0 → (MeromorphicAt (f ∘ g) x ↔ MeromorphicAt f (g x))- Defined in
- Mathlib.Analysis.Meromorphic.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 197 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
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
- CompleteSpacestatement and proof · cited by 2,532
- CharZerostatement and proof · cited by 932
- derivstatement and proof · cited by 676
- AnalyticAtstatement and proof · cited by 321
- MeromorphicAtstatement and proof · cited by 160
- nhdsWithin_le_nhdsproof · cited by 145
- Filter.EventuallyEq.filter_monoproof · cited by 59
- Filter.EventuallyEq.fun_compproof · cited by 47
- MeromorphicAt.congrproof · cited by 12
Cited by2
Results whose statement or proof uses this declaration.
- meromorphicOrderAt_comp_of_deriv_ne_zeroproof · cited by 2
- meromorphicNFAt_comp_iff_of_deriv_ne_zeroproof · cited by 0