Theorems · Theorem · complex analysis

meromorphicNFOn_comp_sub_const_iff_meromorphicNFOn

∀ {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} {U : Set 𝕜},
  MeromorphicNFOn (f ∘ fun x => x - c) U ↔ MeromorphicNFOn f (U - {c})

MeromorphicNFOn is invariant under translation.

Defined in: Mathlib.Analysis.Meromorphic.NormalForm
Cited by: 4 results in Mathlib
Foundations: Depth 201 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: NontriviallyNormedField NormedAddCommGroup NormedSpace

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Cites8

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Setstatement and proof · cited by 53,352
NormedAddCommGroupstatement and proof · cited by 15,752
NormedSpacestatement and proof · cited by 12,499
NontriviallyNormedFieldstatement and proof · cited by 8,742
sub_eq_add_negproof · cited by 1,023
Set.substatement · cited by 136
MeromorphicNFOnstatement and proof · cited by 35
Set.neg_singletonproof · cited by 14

Cited by4

Results whose statement or proof uses this declaration.

meromorphicNFOn_closedBall_comp_sub_const_iff_meromorphicNFOn_closedBallproof · cited by 1
meromorphicNFOn_ball_comp_sub_const_iff_meromorphicNFOn_ballproof · cited by 1
meromorphicNFOn_sphere_comp_sub_const_iff_meromorphicNFOn_sphereproof · cited by 1
meromorphicNFOn_fun_comp_sub_const_iff_meromorphicNFOnproof · cited by 0