Theorems · Theorem · complex analysis
meromorphicNFOn_closedBall_comp_sub_const_iff_meromorphicNFOn_closedBall
∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] {f : 𝕜 → E} {c : 𝕜} {R : ℝ},
MeromorphicNFOn (f ∘ fun x => x - c) (Metric.closedBall c R) ↔ MeromorphicNFOn f (Metric.closedBall 0 R)MeromorphicNFOn is invariant under translation, special case where the set is a closed ball.
- Defined in
- Mathlib.Analysis.Meromorphic.NormalForm
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 202 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- sub_selfproof · cited by 996
- Metric.closedBallstatement and proof · cited by 704
- MeromorphicNFOnstatement and proof · cited by 35
- closedBall_sub_singletonproof · cited by 4
- meromorphicNFOn_comp_sub_const_iff_meromorphicNFOnproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.