Theorems · Theorem · complex analysis
MeromorphicAt.comp_analyticAt
∀ {𝕜 : Type u_1} {𝕜' : Type u_2} [inst : NontriviallyNormedField 𝕜] [inst_1 : NontriviallyNormedField 𝕜']
[inst_2 : NormedAlgebra 𝕜 𝕜'] {F : Type u_5} [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F]
[inst_5 : NormedSpace 𝕜' F] [IsScalarTower 𝕜 𝕜' F] {x : 𝕜} {f : 𝕜' → F} {g : 𝕜 → 𝕜'},
MeromorphicAt f (g x) → AnalyticAt 𝕜 g x → MeromorphicAt (f ∘ g) xThe composition of a meromorphic and an analytic function is meromorphic.
- Defined in
- Mathlib.Analysis.Meromorphic.Basic
- Cited by
- 3 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.
Cites40
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
- IsScalarTowerstatement and proof · cited by 3,896
- Filter.Eventuallyproof · cited by 3,134
- Filter.univ_mem'proof · cited by 1,672
- Filter.mp_memproof · cited by 1,537
- MulActionproof · cited by 1,294
- NormedAlgebrastatement and proof · cited by 1,165
Cited by3
Results whose statement or proof uses this declaration.
- meromorphicAt_comp_add_const_iff_meromorphicAtproof · cited by 4
- meromorphicAt_comp_iff_of_deriv_ne_zeroproof · cited by 2
- MeromorphicAt.meromorphicTrailingCoeffAt_compproof · cited by 1