Update to latest version of mathlib

Nevanlinna/analyticAt.lean

@@ -116,10 +116,10 @@ theorem AnalyticAt.supp_order_toNat
   intro h₁f
   simp [hf.order_eq_zero_iff.2 h₁f]
 
-
+/-
 theorem ContinuousLinearEquiv.analyticAt
   (ℓ : ℂ ≃L[ℂ] ℂ) (z₀ : ℂ) : AnalyticAt ℂ (⇑ℓ) z₀ := ℓ.toContinuousLinearMap.analyticAt z₀
-
+-/
 
 theorem eventually_nhds_comp_composition
   {f₁ f₂ ℓ : ℂ → ℂ}

Nevanlinna/analyticOn_zeroSet.lean

@@ -4,17 +4,17 @@ import Mathlib.Analysis.Complex.Basic
 import Nevanlinna.analyticAt
 
 
-noncomputable def AnalyticOn.order
+noncomputable def AnalyticOnNhd.order
-  {f : ℂ → ℂ} {U : Set ℂ} (hf : AnalyticOn ℂ f U) : U → ℕ∞ := fun u ↦ (hf u u.2).order
+  {f : ℂ → ℂ} {U : Set ℂ} (hf : AnalyticOnNhd ℂ f U) : U → ℕ∞ := fun u ↦ (hf u u.2).order
 
 
-theorem AnalyticOn.order_eq_nat_iff
+theorem AnalyticOnNhd.order_eq_nat_iff
   {f : ℂ → ℂ}
   {U : Set ℂ}
   {z₀ : U}
-  (hf : AnalyticOn ℂ f U)
+  (hf : AnalyticOnNhd ℂ f U)
   (n : ℕ) :
-  hf.order z₀ = ↑n ↔ ∃ (g : ℂ → ℂ), AnalyticOn ℂ g U ∧ g z₀ ≠ 0 ∧ ∀ z, f z = (z - z₀) ^ n • g z := by
+  hf.order z₀ = ↑n ↔ ∃ (g : ℂ → ℂ), AnalyticOnNhd ℂ g U ∧ g z₀ ≠ 0 ∧ ∀ z, f z = (z - z₀) ^ n • g z := by
 
   constructor
   -- Direction →
@@ -91,31 +91,31 @@ theorem AnalyticOn.order_eq_nat_iff
   -- direction ←
   intro h
   obtain ⟨g, h₁g, h₂g, h₃g⟩ := h
-  dsimp [AnalyticOn.order]
+  dsimp [AnalyticOnNhd.order]
   rw [AnalyticAt.order_eq_nat_iff]
   use g
   exact ⟨h₁g z₀ z₀.2, ⟨h₂g, Filter.Eventually.of_forall h₃g⟩⟩
 
 
-theorem AnalyticOn.support_of_order₁
+theorem AnalyticOnNhd.support_of_order₁
   {f : ℂ → ℂ}
   {U : Set ℂ}
-  (hf : AnalyticOn ℂ f U) :
+  (hf : AnalyticOnNhd ℂ f U) :
   Function.support hf.order = U.restrict f⁻¹' {0} := by
   ext u
-  simp [AnalyticOn.order]
+  simp [AnalyticOnNhd.order]
   rw [not_iff_comm, (hf u u.2).order_eq_zero_iff]
 
 
-theorem AnalyticOn.eliminateZeros
+theorem AnalyticOnNhd.eliminateZeros
   {f : ℂ → ℂ}
   {U : Set ℂ}
   {A : Finset U}
-  (hf : AnalyticOn ℂ f U)
+  (hf : AnalyticOnNhd ℂ f U)
   (n : U → ℕ) :
-  (∀ a ∈ A, hf.order a = n a) → ∃ (g : ℂ → ℂ), AnalyticOn ℂ g U ∧ (∀ a ∈ A, g a ≠ 0) ∧ ∀ z, f z = (∏ a ∈ A, (z - a) ^ (n a)) • g z := by
+  (∀ a ∈ A, hf.order a = n a) → ∃ (g : ℂ → ℂ), AnalyticOnNhd ℂ g U ∧ (∀ a ∈ A, g a ≠ 0) ∧ ∀ z, f z = (∏ a ∈ A, (z - a) ^ (n a)) • g z := by
 
-  apply Finset.induction (α := U) (p := fun A ↦ (∀ a ∈ A, (hf a.1 a.2).order = n a) → ∃ (g : ℂ → ℂ), AnalyticOn ℂ g U ∧ (∀ a ∈ A, g a ≠ 0) ∧ ∀ z, f z = (∏ a ∈ A, (z - a) ^ (n a)) • g z)
+  apply Finset.induction (α := U) (p := fun A ↦ (∀ a ∈ A, (hf a.1 a.2).order = n a) → ∃ (g : ℂ → ℂ), AnalyticOnNhd ℂ g U ∧ (∀ a ∈ A, g a ≠ 0) ∧ ∀ z, f z = (∏ a ∈ A, (z - a) ^ (n a)) • g z)
 
   -- case empty
   simp
@@ -146,7 +146,7 @@ theorem AnalyticOn.eliminateZeros
       intro b _
       apply AnalyticAt.pow
       apply AnalyticAt.sub
-      apply analyticAt_id ℂ
+      apply analyticAt_id
       exact analyticAt_const
 
     have h₂φ : h₁φ.order = (0 : ℕ) := by
@@ -173,7 +173,7 @@ theorem AnalyticOn.eliminateZeros
     rw [h₂φ]
     simp
 
-  obtain ⟨g₁, h₁g₁, h₂g₁, h₃g₁⟩ := (AnalyticOn.order_eq_nat_iff h₁g₀ (n b₀)).1 this
+  obtain ⟨g₁, h₁g₁, h₂g₁, h₃g₁⟩ := (AnalyticOnNhd.order_eq_nat_iff h₁g₀ (n b₀)).1 this
 
   use g₁
   constructor
@@ -203,7 +203,7 @@ theorem XX
   {f : ℂ → ℂ}
   {U : Set ℂ}
   (hU : IsPreconnected U)
-  (h₁f : AnalyticOn ℂ f U)
+  (h₁f : AnalyticOnNhd ℂ f U)
   (h₂f : ∃ u ∈ U, f u ≠ 0) :
   ∀ (hu : u ∈ U), (h₁f u hu).order.toNat = (h₁f u hu).order := by
 
@@ -221,7 +221,7 @@ theorem discreteZeros
   {f : ℂ → ℂ}
   {U : Set ℂ}
   (hU : IsPreconnected U)
-  (h₁f : AnalyticOn ℂ f U)
+  (h₁f : AnalyticOnNhd ℂ f U)
   (h₂f : ∃ u ∈ U, f u ≠ 0) :
   DiscreteTopology ((U.restrict f)⁻¹' {0}) := by
 
@@ -293,7 +293,7 @@ theorem finiteZeros
   {U : Set ℂ}
   (h₁U : IsPreconnected U)
   (h₂U : IsCompact U)
-  (h₁f : AnalyticOn ℂ f U)
+  (h₁f : AnalyticOnNhd ℂ f U)
   (h₂f : ∃ u ∈ U, f u ≠ 0) :
   Set.Finite (U.restrict f⁻¹' {0}) := by
 
@@ -310,14 +310,14 @@ theorem finiteZeros
   exact discreteZeros h₁U h₁f h₂f
 
 
-theorem AnalyticOnCompact.eliminateZeros
+theorem AnalyticOnNhdCompact.eliminateZeros
   {f : ℂ → ℂ}
   {U : Set ℂ}
   (h₁U : IsPreconnected U)
   (h₂U : IsCompact U)
-  (h₁f : AnalyticOn ℂ f U)
+  (h₁f : AnalyticOnNhd ℂ f U)
   (h₂f : ∃ u ∈ U, f u ≠ 0) :
-  ∃ (g : ℂ → ℂ) (A : Finset U), AnalyticOn ℂ g U ∧ (∀ z ∈ U, g z ≠ 0) ∧ ∀ z, f z = (∏ a ∈ A, (z - a) ^ (h₁f.order a).toNat) • g z := by
+  ∃ (g : ℂ → ℂ) (A : Finset U), AnalyticOnNhd ℂ g U ∧ (∀ z ∈ U, g z ≠ 0) ∧ ∀ z, f z = (∏ a ∈ A, (z - a) ^ (h₁f.order a).toNat) • g z := by
 
   let A := (finiteZeros h₁U h₂U h₁f h₂f).toFinset
 
@@ -325,13 +325,13 @@ theorem AnalyticOnCompact.eliminateZeros
 
   have hn : ∀ a ∈ A, (h₁f a a.2).order = n a := by
     intro a _
-    dsimp [n, AnalyticOn.order]
+    dsimp [n, AnalyticOnNhd.order]
     rw [eq_comm]
     apply XX h₁U
     exact h₂f
 
 
-  obtain ⟨g, h₁g, h₂g, h₃g⟩ := AnalyticOn.eliminateZeros (A := A) h₁f n hn
+  obtain ⟨g, h₁g, h₂g, h₃g⟩ := AnalyticOnNhd.eliminateZeros (A := A) h₁f n hn
   use g
   use A
 
@@ -357,14 +357,14 @@ theorem AnalyticOnCompact.eliminateZeros
     · exact inter
 
 
-theorem AnalyticOnCompact.eliminateZeros₂
+theorem AnalyticOnNhdCompact.eliminateZeros₂
   {f : ℂ → ℂ}
   {U : Set ℂ}
   (h₁U : IsPreconnected U)
   (h₂U : IsCompact U)
-  (h₁f : AnalyticOn ℂ f U)
+  (h₁f : AnalyticOnNhd ℂ f U)
   (h₂f : ∃ u ∈ U, f u ≠ 0) :
-  ∃ (g : ℂ → ℂ), AnalyticOn ℂ g U ∧ (∀ z ∈ U, g z ≠ 0) ∧ ∀ z, f z = (∏ a ∈ (finiteZeros h₁U h₂U h₁f h₂f).toFinset, (z - a) ^ (h₁f.order a).toNat) • g z := by
+  ∃ (g : ℂ → ℂ), AnalyticOnNhd ℂ g U ∧ (∀ z ∈ U, g z ≠ 0) ∧ ∀ z, f z = (∏ a ∈ (finiteZeros h₁U h₂U h₁f h₂f).toFinset, (z - a) ^ (h₁f.order a).toNat) • g z := by
 
   let A := (finiteZeros h₁U h₂U h₁f h₂f).toFinset
 
@@ -372,12 +372,12 @@ theorem AnalyticOnCompact.eliminateZeros₂
 
   have hn : ∀ a ∈ A, (h₁f a a.2).order = n a := by
     intro a _
-    dsimp [n, AnalyticOn.order]
+    dsimp [n, AnalyticOnNhd.order]
     rw [eq_comm]
     apply XX h₁U
     exact h₂f
 
-  obtain ⟨g, h₁g, h₂g, h₃g⟩ := AnalyticOn.eliminateZeros (A := A) h₁f n hn
+  obtain ⟨g, h₁g, h₂g, h₃g⟩ := AnalyticOnNhd.eliminateZeros (A := A) h₁f n hn
   use g
 
   have inter : ∀ (z : ℂ), f z = (∏ a ∈ A, (z - ↑a) ^ (h₁f (↑a) a.property).order.toNat) • g z := by
@@ -402,14 +402,14 @@ theorem AnalyticOnCompact.eliminateZeros₂
     · exact h₃g
 
 
-theorem AnalyticOnCompact.eliminateZeros₁
+theorem AnalyticOnNhdCompact.eliminateZeros₁
   {f : ℂ → ℂ}
   {U : Set ℂ}
   (h₁U : IsPreconnected U)
   (h₂U : IsCompact U)
-  (h₁f : AnalyticOn ℂ f U)
+  (h₁f : AnalyticOnNhd ℂ f U)
   (h₂f : ∃ u ∈ U, f u ≠ 0) :
-  ∃ (g : ℂ → ℂ), AnalyticOn ℂ g U ∧ (∀ z ∈ U, g z ≠ 0) ∧ ∀ z, f z = (∏ᶠ a, (z - a) ^ (h₁f.order a).toNat) • g z := by
+  ∃ (g : ℂ → ℂ), AnalyticOnNhd ℂ g U ∧ (∀ z ∈ U, g z ≠ 0) ∧ ∀ z, f z = (∏ᶠ a, (z - a) ^ (h₁f.order a).toNat) • g z := by
 
   let A := (finiteZeros h₁U h₂U h₁f h₂f).toFinset
 
@@ -417,12 +417,12 @@ theorem AnalyticOnCompact.eliminateZeros₁
 
   have hn : ∀ a ∈ A, (h₁f a a.2).order = n a := by
     intro a _
-    dsimp [n, AnalyticOn.order]
+    dsimp [n, AnalyticOnNhd.order]
     rw [eq_comm]
     apply XX h₁U
     exact h₂f
 
-  obtain ⟨g, h₁g, h₂g, h₃g⟩ := AnalyticOn.eliminateZeros (A := A) h₁f n hn
+  obtain ⟨g, h₁g, h₂g, h₃g⟩ := AnalyticOnNhd.eliminateZeros (A := A) h₁f n hn
   use g
 
   have inter : ∀ (z : ℂ), f z = (∏ a ∈ A, (z - ↑a) ^ (h₁f (↑a) a.property).order.toNat) • g z := by

Nevanlinna/bilinear.lean

@@ -28,7 +28,7 @@ orthonormal basis `v` as `∑ i, (v i) ⊗ₜ[ℝ] (v i)`.
 
 -/
 
-
+open InnerProductSpace
 open TensorProduct
 
 
@@ -41,12 +41,11 @@ noncomputable def InnerProductSpace.canonicalCovariantTensor
   (E : Type*) [NormedAddCommGroup E] [InnerProductSpace ℝ E] [FiniteDimensional ℝ E]
   : E ⊗[ℝ] E := ∑ i, ((stdOrthonormalBasis ℝ E) i) ⊗ₜ[ℝ] ((stdOrthonormalBasis ℝ E) i)
 
-
 theorem InnerProductSpace.canonicalCovariantTensorRepresentation
   (E : Type*) [NormedAddCommGroup E] [InnerProductSpace ℝ E] [FiniteDimensional ℝ E]
   [Fintype ι]
-  (v : OrthonormalBasis ι ℝ E)
+  (v : OrthonormalBasis ι ℝ E) :
-  : InnerProductSpace.canonicalCovariantTensor E = ∑ i, (v i) ⊗ₜ[ℝ] (v i) := by
+  InnerProductSpace.canonicalCovariantTensor E = ∑ i, (v i) ⊗ₜ[ℝ] (v i) := by
 
   let w := stdOrthonormalBasis ℝ E
   conv =>

Nevanlinna/divisor.lean

@@ -1,5 +1,13 @@
+import Mathlib.Analysis.SpecialFunctions.Integrals
+import Mathlib.Analysis.SpecialFunctions.Log.NegMulLog
+import Mathlib.Analysis.Convex.SpecificFunctions.Deriv
 import Nevanlinna.analyticAt
 
+open scoped Interval Topology
+open Real Filter MeasureTheory intervalIntegral
+
+
+
 
 structure Divisor where
   toFun : ℂ → ℤ
@@ -48,10 +56,10 @@ theorem Divisor.support_cap_compact
   exact Set.inter_subset_right
 
 
-noncomputable def AnalyticOn.zeroDivisor
+noncomputable def AnalyticOnNhd.zeroDivisor
   {f : ℂ → ℂ}
   {U : Set ℂ}
-  (hf : AnalyticOn ℂ f U) :
+  (hf : AnalyticOnNhd ℂ f U) :
   Divisor where
 
     toFun := by
@@ -124,28 +132,28 @@ noncomputable def AnalyticOn.zeroDivisor
       tauto
 
 
-theorem AnalyticOn.support_of_zeroDivisor
+theorem AnalyticOnNhd.support_of_zeroDivisor
   {f : ℂ → ℂ}
   {U : Set ℂ}
-  (hf : AnalyticOn ℂ f U) :
+  (hf : AnalyticOnNhd ℂ f U) :
   Function.support hf.zeroDivisor ⊆ U := by
 
   intro z
   contrapose
   intro hz
-  dsimp [AnalyticOn.zeroDivisor]
+  dsimp [AnalyticOnNhd.zeroDivisor]
   simp
   tauto
 
 
-theorem AnalyticOn.support_of_zeroDivisor₂
+theorem AnalyticOnNhd.support_of_zeroDivisor₂
   {f : ℂ → ℂ}
   {U : Set ℂ}
-  (hf : AnalyticOn ℂ f U) :
+  (hf : AnalyticOnNhd ℂ f U) :
   Function.support hf.zeroDivisor ⊆ f⁻¹' {0} := by
 
   intro z hz
-  dsimp [AnalyticOn.zeroDivisor] at hz
+  dsimp [AnalyticOnNhd.zeroDivisor] at hz
   have t₀ := hf.support_of_zeroDivisor hz
   simp [hf.support_of_zeroDivisor hz] at hz
   let A := hz.1

Nevanlinna/holomorphic_JensenFormula.lean

@@ -11,7 +11,7 @@ open Real
 
 theorem jensen_case_R_eq_one
   (f : ℂ → ℂ)
-  (h₁f : AnalyticOn ℂ f (Metric.closedBall 0 1))
+  (h₁f : AnalyticOnNhd ℂ f (Metric.closedBall 0 1))
   (h₂f : f 0 ≠ 0) :
   log ‖f 0‖ = -∑ᶠ s, (h₁f.order s).toNat * log (‖s.1‖⁻¹) + (2 * π)⁻¹ * ∫ (x : ℝ) in (0)..(2 * π), log ‖f (circleMap 0 1 x)‖ := by
 
@@ -24,7 +24,7 @@ theorem jensen_case_R_eq_one
   have h'₂f : ∃ u ∈ (Metric.closedBall (0 : ℂ) 1), f u ≠ 0 := by
     use 0; simp; exact h₂f
 
-  obtain ⟨F, h₁F, h₂F, h₃F⟩ := AnalyticOnCompact.eliminateZeros₂ h₁U h₂U h₁f h'₂f
+  obtain ⟨F, h₁F, h₂F, h₃F⟩ := AnalyticOnNhdCompact.eliminateZeros₂ h₁U h₂U h₁f h'₂f
 
   have h'₁F : ∀ z ∈ Metric.closedBall (0 : ℂ) 1, HolomorphicAt F z := by
     intro z h₁z
@@ -259,9 +259,9 @@ theorem jensen_case_R_eq_one
   intro x ⟨h₁x, _⟩
   simp
 
-  dsimp [AnalyticOn.order] at h₁x
+  dsimp [AnalyticOnNhd.order] at h₁x
   simp only [Function.mem_support, ne_eq, Nat.cast_eq_zero, not_or] at h₁x
-  exact AnalyticAt.supp_order_toNat (AnalyticOn.order.proof_1 h₁f x) h₁x
+  exact AnalyticAt.supp_order_toNat (AnalyticOnNhd.order.proof_1 h₁f x) h₁x
 
   --
   intro x hx
@@ -297,7 +297,7 @@ theorem jensen
   {R : ℝ}
   (hR : 0 < R)
   (f : ℂ → ℂ)
-  (h₁f : AnalyticOn ℂ f (Metric.closedBall 0 R))
+  (h₁f : AnalyticOnNhd ℂ f (Metric.closedBall 0 R))
   (h₂f : f 0 ≠ 0) :
   log ‖f 0‖ = -∑ᶠ s, (h₁f.order s).toNat * log (R * ‖s.1‖⁻¹) + (2 * π)⁻¹ * ∫ (x : ℝ) in (0)..(2 * π), log ‖f (circleMap 0 R x)‖ := by
 
@@ -327,8 +327,8 @@ theorem jensen
 
   let F := f ∘ ℓ
 
-  have h₁F : AnalyticOn ℂ F (Metric.closedBall 0 1) := by
+  have h₁F : AnalyticOnNhd ℂ F (Metric.closedBall 0 1) := by
-    apply AnalyticOn.comp (t := Metric.closedBall 0 R)
+    apply AnalyticOnNhd.comp (t := Metric.closedBall 0 R)
     exact h₁f
     intro x _
     apply ℓ.toContinuousLinearMap.analyticAt x
@@ -430,7 +430,7 @@ theorem jensen
   left
   congr 1
 
-  dsimp [AnalyticOn.order]
+  dsimp [AnalyticOnNhd.order]
   rw [← AnalyticAt.order_comp_CLE ℓ]
 
   --

Nevanlinna/holomorphic_zero.lean

@@ -134,7 +134,7 @@ theorem topOnPreconnected
   {f : ℂ → ℂ}
   {U : Set ℂ}
   (hU : IsPreconnected U)
-  (h₁f : AnalyticOn ℂ f U)
+  (h₁f : AnalyticOnNhd ℂ f U)
   (h₂f : ∃ z ∈ U, f z ≠ 0) :
   ∀ (hz : z ∈ U), (h₁f z hz).order ≠ ⊤ := by
 
@@ -143,7 +143,7 @@ theorem topOnPreconnected
   obtain ⟨z', hz'⟩ := H
   rw [AnalyticAt.order_eq_top_iff] at hz'
   rw [← AnalyticAt.frequently_zero_iff_eventually_zero (h₁f z z')] at hz'
-  have A := AnalyticOn.eqOn_zero_of_preconnected_of_frequently_eq_zero h₁f hU z' hz'
+  have A := AnalyticOnNhd.eqOn_zero_of_preconnected_of_frequently_eq_zero h₁f hU z' hz'
   tauto
 
 
@@ -151,7 +151,7 @@ theorem supportZeroSet
   {f : ℂ → ℂ}
   {U : Set ℂ}
   (hU : IsPreconnected U)
-  (h₁f : AnalyticOn ℂ f U)
+  (h₁f : AnalyticOnNhd ℂ f U)
   (h₂f : ∃ z ∈ U, f z ≠ 0) :
   U ∩ Function.support (zeroDivisor f) = U ∩ f⁻¹' {0} := by
 
@@ -180,7 +180,7 @@ theorem supportZeroSet
           refine Eq.symm (ENat.coe_toNat ?h.mpr.right.right.right.a)
           exact topOnPreconnected hU h₁f h₂f h₁x
 
-
+/-
 theorem discreteZeros
   {f : ℂ → ℂ} :
   DiscreteTopology (Function.support (zeroDivisor f)) := by
@@ -254,13 +254,13 @@ theorem discreteZeros
   simp [this] at F
   ext
   rwa [sub_eq_zero] at F
-
+-/
 
 theorem zeroDivisor_finiteOnCompact
   {f : ℂ → ℂ}
   {U : Set ℂ}
   (hU : IsPreconnected U)
-  (h₁f : AnalyticOn ℂ f U)
+  (h₁f : AnalyticOnNhd ℂ f U)
   (h₂f : ∃ z ∈ U, f z ≠ 0) -- not needed!
   (h₂U : IsCompact U) :
   Set.Finite (U ∩ Function.support (zeroDivisor f)) := by
@@ -289,7 +289,7 @@ noncomputable def zeroDivisorDegree
   {U : Set ℂ}
   (h₁U : IsPreconnected U) -- not needed!
   (h₂U : IsCompact U)
-  (h₁f : AnalyticOn ℂ f U)
+  (h₁f : AnalyticOnNhd ℂ f U)
   (h₂f : ∃ z ∈ U, f z ≠ 0) : -- not needed!
   ℕ := (zeroDivisor_finiteOnCompact h₁U h₁f h₂f h₂U).toFinset.card
 
@@ -299,7 +299,7 @@ lemma zeroDivisorDegreeZero
   {U : Set ℂ}
   (h₁U : IsPreconnected U) -- not needed!
   (h₂U : IsCompact U)
-  (h₁f : AnalyticOn ℂ f U)
+  (h₁f : AnalyticOnNhd ℂ f U)
   (h₂f : ∃ z ∈ U, f z ≠ 0) : -- not needed!
   0 = zeroDivisorDegree h₁U h₂U h₁f h₂f ↔ U ∩ (zeroDivisor f).support = ∅ := by
   sorry
@@ -309,9 +309,9 @@ lemma eliminatingZeros₀
   {U : Set ℂ}
   (h₁U : IsPreconnected U)
   (h₂U : IsCompact U) :
-  ∀ n : ℕ, ∀ f : ℂ → ℂ, (h₁f : AnalyticOn ℂ f U) → (h₂f : ∃ z ∈ U, f z ≠ 0) →
+  ∀ n : ℕ, ∀ f : ℂ → ℂ, (h₁f : AnalyticOnNhd ℂ f U) → (h₂f : ∃ z ∈ U, f z ≠ 0) →
   (n = zeroDivisorDegree h₁U h₂U h₁f h₂f) →
-  ∃ F : ℂ → ℂ, (AnalyticOn ℂ F U) ∧ (f = F * ∏ᶠ a ∈ (U ∩ (zeroDivisor f).support), fun z ↦ (z - a) ^ (zeroDivisor f a)) := by
+  ∃ F : ℂ → ℂ, (AnalyticOnNhd ℂ F U) ∧ (f = F * ∏ᶠ a ∈ (U ∩ (zeroDivisor f).support), fun z ↦ (z - a) ^ (zeroDivisor f a)) := by
 
   intro n
   induction' n with n ih
@@ -340,7 +340,7 @@ lemma eliminatingZeros₀
 
 
 
-  let A := AnalyticOn.order_eq_nat_iff h₁f hz₀.1 (zeroDivisor f z₀)
+  let A := AnalyticOnNhd.order_eq_nat_iff h₁f hz₀.1 (zeroDivisor f z₀)
   let B := zeroDivisor_eq_ord_AtZeroDivisorSupport hz₀.2
   let B := zeroDivisor_eq_ord_AtZeroDivisorSupport' hz₀.2
   rw [eq_comm] at B

lake-manifest.json

@@ -5,7 +5,7 @@
    "type": "git",
    "subDir": null,
    "scope": "leanprover-community",
-   "rev": "46fed98b5cac2b1ea64e363b420c382ed1af0d85",
+   "rev": "bf12ff6041cbab6eba6b54d9467baed807bb2bfd",
    "name": "batteries",
    "manifestFile": "lake-manifest.json",
    "inputRev": "main",
@@ -25,7 +25,7 @@
    "type": "git",
    "subDir": null,
    "scope": "leanprover-community",
-   "rev": "662f986ad3c5ad6ab1a1726b3c04f5ec425aa9f7",
+   "rev": "50aaaf78b7db5bd635c19c660d59ed31b9bc9b5a",
    "name": "aesop",
    "manifestFile": "lake-manifest.json",
    "inputRev": "master",
@@ -61,11 +61,11 @@
    "inputRev": "main",
    "inherited": true,
    "configFile": "lakefile.toml"},
-  {"url": "https://github.com/siddhartha-gadgil/LeanSearchClient.git",
+  {"url": "https://github.com/leanprover-community/LeanSearchClient",
    "type": "git",
    "subDir": null,
-   "scope": "",
+   "scope": "leanprover-community",
-   "rev": "c260ed920e2ebd23ef9fc8ca3fd24115e04c18b1",
+   "rev": "2ba60fa2c384a94735454db11a2d523612eaabff",
    "name": "LeanSearchClient",
    "manifestFile": "lake-manifest.json",
    "inputRev": "main",
@@ -75,7 +75,7 @@
    "type": "git",
    "subDir": null,
    "scope": "",
-   "rev": "4e40837aec257729b3c38dc3e635fc64a7a8a8c1",
+   "rev": "eed3300c27c9f168d53e13bb198a92a147b671d0",
    "name": "mathlib",
    "manifestFile": "lake-manifest.json",
    "inputRev": null,