Update stronglyMeromorphic.lean
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@ -63,28 +63,17 @@ theorem StronglyMeromorphicAt.analytic
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exact h₁g
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exact h₁g
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/- Make strongly MeromorphicAt -/
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/- Make strongly MeromorphicAt -/
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noncomputable def MeromorphicAt.makeStronglyMeromorphicAt
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def MeromorphicAt.makeStronglyMeromorphicAt
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{f : ℂ → ℂ}
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{f : ℂ → ℂ}
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{z₀ : ℂ}
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{z₀ : ℂ}
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(hf : MeromorphicAt f z₀) :
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(hf : MeromorphicAt f z₀) :
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ℂ → ℂ := by
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ℂ → ℂ := by
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by_cases h₂f : hf.order = ⊤
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by_cases h₂f : hf.order = 0
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· have : (0 : WithTop ℤ) = (0 : ℤ) := rfl
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rw [this, hf.order_eq_int_iff] at h₂f
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exact Classical.choose h₂f
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· exact 0
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· exact 0
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· have : ∃ n : ℤ, hf.order = n := by
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exact Option.ne_none_iff_exists'.mp h₂f
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let o := hf.order.untop h₂f
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have : hf.order = o := by
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exact Eq.symm (WithTop.coe_untop hf.order h₂f)
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rw [MeromorphicAt.order_eq_int_iff] at this
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obtain ⟨g, hg⟩ := this
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exact fun z ↦ (z - z₀) ^ o • g z
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sorry
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theorem StronglyMeromorphicAt_of_makeStronglyMeromorphic
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theorem StronglyMeromorphicAt_of_makeStronglyMeromorphic
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@ -92,6 +81,7 @@ theorem StronglyMeromorphicAt_of_makeStronglyMeromorphic
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{z₀ : ℂ}
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{z₀ : ℂ}
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(hf : MeromorphicAt f z₀) :
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(hf : MeromorphicAt f z₀) :
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StronglyMeromorphicAt hf.makeStronglyMeromorphic z₀ := by
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StronglyMeromorphicAt hf.makeStronglyMeromorphic z₀ := by
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sorry
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sorry
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