Theorems · Theorem · complex analysis
meromorphicAt_comp_add_const_iff_meromorphicAt
∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_3} [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] {x c : 𝕜} {f : 𝕜 → E}, MeromorphicAt (f ∘ fun x => x + c) x ↔ MeromorphicAt f (x + c)MeromorphicAt is invariant under translation.
- Defined in
- Mathlib.Analysis.Meromorphic.Basic
- Cited by
- 4 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.
Cites10
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
- sub_add_cancelproof · cited by 344
- MeromorphicAtstatement and proof · cited by 160
- analyticAt_constproof · cited by 70
- analyticAt_idproof · cited by 39
- AnalyticAt.fun_subproof · cited by 29
- AnalyticAt.fun_addproof · cited by 9
- MeromorphicAt.comp_analyticAtproof · cited by 3
Cited by4
Results whose statement or proof uses this declaration.
- MeromorphicOn.meromorphicOn_comp_add_const_iff_meromorphicOnproof · cited by 2
- meromorphicOrderAt_comp_add_const_eq_meromorphicOrderAtproof · cited by 2
- meromorphicTrailingCoeffAt_comp_add_const_eq_meromorphicTrailingCoeffAtproof · cited by 1
- meromorphicAt_fun_comp_add_const_iff_meromorphicAtproof · cited by 0