Theorems · Theorem · complex analysis
MeromorphicNFAt.comp_analyticAt
∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] {f : 𝕜 → E} {g : 𝕜 → 𝕜} {x : 𝕜},
MeromorphicNFAt f (g x) → AnalyticAt 𝕜 g x → MeromorphicNFAt (f ∘ g) xThe composition of a meromorphic function in normal form and an analytic function is meromorphic in normal form.
- Defined in
- Mathlib.Analysis.Meromorphic.NormalForm
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 196 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
- Top.topproof · cited by 9,680
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- Set.ofPredproof · cited by 6,101
- nhdsproof · cited by 5,554
- Set.preimageproof · cited by 4,946
- Filter.Eventuallyproof · cited by 3,134
- mul_commproof · cited by 2,262
- Filter.EventuallyEqproof · cited by 1,912
- Filter.univ_mem'proof · cited by 1,672
- Filter.mp_memproof · cited by 1,537
Cited by1
Results whose statement or proof uses this declaration.
- meromorphicNFAt_comp_add_const_iff_meromorphicNFAtproof · cited by 2