Theorems · Theorem · complex analysis
meromorphicAt_smul_iff_of_ne_zero
∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_3} [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] {g : 𝕜 → 𝕜} {x : 𝕜} {f : 𝕜 → E},
AnalyticAt 𝕜 g x → g x ≠ 0 → (MeromorphicAt (g • f) x ↔ MeromorphicAt f x)- Defined in
- Mathlib.Analysis.Meromorphic.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 192 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
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
- Filter.univ_mem'proof · cited by 1,672
- Filter.mp_memproof · cited by 1,537
- MulActionproof · cited by 1,294
- AnalyticAtstatement and proof · cited by 321
- MeromorphicAtstatement and proof · cited by 160
- nhdsWithin_le_nhdsproof · cited by 145
- Filter.Tendsto.mono_leftproof · cited by 125
- inv_smul_smul₀proof · cited by 80
- AnalyticAt.continuousAtproof · cited by 35
Cited by2
Results whose statement or proof uses this declaration.
- meromorphicOrderAt_smul_of_ne_zeroproof · cited by 1
- meromorphicAt_mul_iff_of_ne_zeroproof · cited by 0