Theorems · Theorem · complex analysis
MeromorphicAt.deriv
∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_3} [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] [CompleteSpace E] {f : 𝕜 → E} {x : 𝕜}, MeromorphicAt f x → MeromorphicAt (deriv f) xDerivatives of meromorphic functions are meromorphic.
- Defined in
- Mathlib.Analysis.Meromorphic.Basic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 198 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites37
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.Eventuallyproof · cited by 3,134
- Compl.complproof · cited by 2,925
- CompleteSpacestatement and proof · cited by 2,532
- nhdsWithinproof · cited by 1,912
- Filter.EventuallyEqproof · cited by 1,912
- Filter.univ_mem'proof · cited by 1,672
- Filter.mp_memproof · cited by 1,537
- add_commproof · cited by 1,535
- derivstatement and proof · cited by 676
Cited by6
Results whose statement or proof uses this declaration.
- meromorphicOrderAt_deriv_eq_sub_oneproof · cited by 2
- Meromorphic.derivproof · cited by 2
- MeromorphicAt.iterated_derivproof · cited by 2
- MeromorphicOn.derivproof · cited by 1
- MeromorphicAt.logDerivproof · cited by 0
- meromorphicOrderAt_logDeriv_eq_neg_oneproof · cited by 0