21 lines
582 B
Lean4
21 lines
582 B
Lean4
import Mathlib.Analysis.Meromorphic.Basic
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import Mathlib.Analysis.Meromorphic.Order
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open MeromorphicOn Metric Real Set Classical
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variable
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{𝕜 : Type*} [NontriviallyNormedField 𝕜] [CompleteSpace 𝕜]
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/-- Derivatives of meromorphic functions are meromorphic. -/
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theorem meromorphicAt_deriv_of_order_eq_top {f : 𝕜 → 𝕜} {x : 𝕜}
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(h : MeromorphicAt f x) (h₁ : h.order ≠ ⊤) :
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MeromorphicAt (deriv f) x := by
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have := h.eventually_analyticAt
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obtain ⟨n, hn⟩ := h
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let g : 𝕜 → 𝕜 := sorry
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rw [MeromorphicAt.meromorphicAt_congr]
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sorry
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