Update to latest version of mathlib
This commit is contained in:
Stefan Kebekus
parent
1a8bde51eb
commit
c8f4cf12ca
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@ -116,10 +116,10 @@ theorem AnalyticAt.supp_order_toNat
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intro h₁f
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simp [hf.order_eq_zero_iff.2 h₁f]
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/-
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theorem ContinuousLinearEquiv.analyticAt
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(ℓ : ℂ ≃L[ℂ] ℂ) (z₀ : ℂ) : AnalyticAt ℂ (⇑ℓ) z₀ := ℓ.toContinuousLinearMap.analyticAt z₀
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-/
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theorem eventually_nhds_comp_composition
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{f₁ f₂ ℓ : ℂ → ℂ}
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@ -4,17 +4,17 @@ import Mathlib.Analysis.Complex.Basic
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import Nevanlinna.analyticAt
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noncomputable def AnalyticOn.order
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{f : ℂ → ℂ} {U : Set ℂ} (hf : AnalyticOn ℂ f U) : U → ℕ∞ := fun u ↦ (hf u u.2).order
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noncomputable def AnalyticOnNhd.order
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{f : ℂ → ℂ} {U : Set ℂ} (hf : AnalyticOnNhd ℂ f U) : U → ℕ∞ := fun u ↦ (hf u u.2).order
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theorem AnalyticOn.order_eq_nat_iff
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theorem AnalyticOnNhd.order_eq_nat_iff
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{f : ℂ → ℂ}
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{U : Set ℂ}
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{z₀ : U}
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(hf : AnalyticOn ℂ f U)
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(hf : AnalyticOnNhd ℂ f U)
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(n : ℕ) :
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hf.order z₀ = ↑n ↔ ∃ (g : ℂ → ℂ), AnalyticOn ℂ g U ∧ g z₀ ≠ 0 ∧ ∀ z, f z = (z - z₀) ^ n • g z := by
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hf.order z₀ = ↑n ↔ ∃ (g : ℂ → ℂ), AnalyticOnNhd ℂ g U ∧ g z₀ ≠ 0 ∧ ∀ z, f z = (z - z₀) ^ n • g z := by
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constructor
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-- Direction →
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@ -91,31 +91,31 @@ theorem AnalyticOn.order_eq_nat_iff
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-- direction ←
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intro h
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obtain ⟨g, h₁g, h₂g, h₃g⟩ := h
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dsimp [AnalyticOn.order]
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dsimp [AnalyticOnNhd.order]
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rw [AnalyticAt.order_eq_nat_iff]
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use g
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exact ⟨h₁g z₀ z₀.2, ⟨h₂g, Filter.Eventually.of_forall h₃g⟩⟩
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theorem AnalyticOn.support_of_order₁
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theorem AnalyticOnNhd.support_of_order₁
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{f : ℂ → ℂ}
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{U : Set ℂ}
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(hf : AnalyticOn ℂ f U) :
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(hf : AnalyticOnNhd ℂ f U) :
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Function.support hf.order = U.restrict f⁻¹' {0} := by
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ext u
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simp [AnalyticOn.order]
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simp [AnalyticOnNhd.order]
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rw [not_iff_comm, (hf u u.2).order_eq_zero_iff]
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theorem AnalyticOn.eliminateZeros
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theorem AnalyticOnNhd.eliminateZeros
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{f : ℂ → ℂ}
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{U : Set ℂ}
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{A : Finset U}
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(hf : AnalyticOn ℂ f U)
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(hf : AnalyticOnNhd ℂ f U)
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(n : U → ℕ) :
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(∀ 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
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(∀ 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
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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)
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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)
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-- case empty
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simp
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@ -146,7 +146,7 @@ theorem AnalyticOn.eliminateZeros
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intro b _
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apply AnalyticAt.pow
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apply AnalyticAt.sub
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apply analyticAt_id ℂ
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apply analyticAt_id
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exact analyticAt_const
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have h₂φ : h₁φ.order = (0 : ℕ) := by
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@ -173,7 +173,7 @@ theorem AnalyticOn.eliminateZeros
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rw [h₂φ]
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simp
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obtain ⟨g₁, h₁g₁, h₂g₁, h₃g₁⟩ := (AnalyticOn.order_eq_nat_iff h₁g₀ (n b₀)).1 this
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obtain ⟨g₁, h₁g₁, h₂g₁, h₃g₁⟩ := (AnalyticOnNhd.order_eq_nat_iff h₁g₀ (n b₀)).1 this
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use g₁
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constructor
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@ -203,7 +203,7 @@ theorem XX
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{f : ℂ → ℂ}
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{U : Set ℂ}
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(hU : IsPreconnected U)
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(h₁f : AnalyticOn ℂ f U)
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(h₁f : AnalyticOnNhd ℂ f U)
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(h₂f : ∃ u ∈ U, f u ≠ 0) :
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∀ (hu : u ∈ U), (h₁f u hu).order.toNat = (h₁f u hu).order := by
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@ -221,7 +221,7 @@ theorem discreteZeros
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{f : ℂ → ℂ}
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{U : Set ℂ}
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(hU : IsPreconnected U)
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(h₁f : AnalyticOn ℂ f U)
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(h₁f : AnalyticOnNhd ℂ f U)
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(h₂f : ∃ u ∈ U, f u ≠ 0) :
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DiscreteTopology ((U.restrict f)⁻¹' {0}) := by
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@ -293,7 +293,7 @@ theorem finiteZeros
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{U : Set ℂ}
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(h₁U : IsPreconnected U)
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(h₂U : IsCompact U)
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(h₁f : AnalyticOn ℂ f U)
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(h₁f : AnalyticOnNhd ℂ f U)
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(h₂f : ∃ u ∈ U, f u ≠ 0) :
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Set.Finite (U.restrict f⁻¹' {0}) := by
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@ -310,14 +310,14 @@ theorem finiteZeros
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exact discreteZeros h₁U h₁f h₂f
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theorem AnalyticOnCompact.eliminateZeros
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theorem AnalyticOnNhdCompact.eliminateZeros
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{f : ℂ → ℂ}
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{U : Set ℂ}
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(h₁U : IsPreconnected U)
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(h₂U : IsCompact U)
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(h₁f : AnalyticOn ℂ f U)
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(h₁f : AnalyticOnNhd ℂ f U)
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(h₂f : ∃ u ∈ U, f u ≠ 0) :
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∃ (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
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∃ (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
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let A := (finiteZeros h₁U h₂U h₁f h₂f).toFinset
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@ -325,13 +325,13 @@ theorem AnalyticOnCompact.eliminateZeros
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have hn : ∀ a ∈ A, (h₁f a a.2).order = n a := by
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intro a _
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dsimp [n, AnalyticOn.order]
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dsimp [n, AnalyticOnNhd.order]
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rw [eq_comm]
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apply XX h₁U
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exact h₂f
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obtain ⟨g, h₁g, h₂g, h₃g⟩ := AnalyticOn.eliminateZeros (A := A) h₁f n hn
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obtain ⟨g, h₁g, h₂g, h₃g⟩ := AnalyticOnNhd.eliminateZeros (A := A) h₁f n hn
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use g
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use A
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@ -357,14 +357,14 @@ theorem AnalyticOnCompact.eliminateZeros
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· exact inter
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theorem AnalyticOnCompact.eliminateZeros₂
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theorem AnalyticOnNhdCompact.eliminateZeros₂
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{f : ℂ → ℂ}
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{U : Set ℂ}
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(h₁U : IsPreconnected U)
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(h₂U : IsCompact U)
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(h₁f : AnalyticOn ℂ f U)
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(h₁f : AnalyticOnNhd ℂ f U)
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(h₂f : ∃ u ∈ U, f u ≠ 0) :
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∃ (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
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∃ (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
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let A := (finiteZeros h₁U h₂U h₁f h₂f).toFinset
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@ -372,12 +372,12 @@ theorem AnalyticOnCompact.eliminateZeros₂
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have hn : ∀ a ∈ A, (h₁f a a.2).order = n a := by
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intro a _
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dsimp [n, AnalyticOn.order]
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dsimp [n, AnalyticOnNhd.order]
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rw [eq_comm]
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apply XX h₁U
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exact h₂f
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obtain ⟨g, h₁g, h₂g, h₃g⟩ := AnalyticOn.eliminateZeros (A := A) h₁f n hn
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obtain ⟨g, h₁g, h₂g, h₃g⟩ := AnalyticOnNhd.eliminateZeros (A := A) h₁f n hn
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use g
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have inter : ∀ (z : ℂ), f z = (∏ a ∈ A, (z - ↑a) ^ (h₁f (↑a) a.property).order.toNat) • g z := by
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@ -402,14 +402,14 @@ theorem AnalyticOnCompact.eliminateZeros₂
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· exact h₃g
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theorem AnalyticOnCompact.eliminateZeros₁
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theorem AnalyticOnNhdCompact.eliminateZeros₁
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{f : ℂ → ℂ}
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{U : Set ℂ}
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(h₁U : IsPreconnected U)
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(h₂U : IsCompact U)
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(h₁f : AnalyticOn ℂ f U)
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(h₁f : AnalyticOnNhd ℂ f U)
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(h₂f : ∃ u ∈ U, f u ≠ 0) :
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∃ (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
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∃ (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
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let A := (finiteZeros h₁U h₂U h₁f h₂f).toFinset
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@ -417,12 +417,12 @@ theorem AnalyticOnCompact.eliminateZeros₁
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have hn : ∀ a ∈ A, (h₁f a a.2).order = n a := by
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intro a _
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dsimp [n, AnalyticOn.order]
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dsimp [n, AnalyticOnNhd.order]
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rw [eq_comm]
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apply XX h₁U
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exact h₂f
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obtain ⟨g, h₁g, h₂g, h₃g⟩ := AnalyticOn.eliminateZeros (A := A) h₁f n hn
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obtain ⟨g, h₁g, h₂g, h₃g⟩ := AnalyticOnNhd.eliminateZeros (A := A) h₁f n hn
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use g
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have inter : ∀ (z : ℂ), f z = (∏ a ∈ A, (z - ↑a) ^ (h₁f (↑a) a.property).order.toNat) • g z := by
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@ -28,7 +28,7 @@ orthonormal basis `v` as `∑ i, (v i) ⊗ₜ[ℝ] (v i)`.
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-/
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open InnerProductSpace
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open TensorProduct
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@ -41,12 +41,11 @@ noncomputable def InnerProductSpace.canonicalCovariantTensor
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(E : Type*) [NormedAddCommGroup E] [InnerProductSpace ℝ E] [FiniteDimensional ℝ E]
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: E ⊗[ℝ] E := ∑ i, ((stdOrthonormalBasis ℝ E) i) ⊗ₜ[ℝ] ((stdOrthonormalBasis ℝ E) i)
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theorem InnerProductSpace.canonicalCovariantTensorRepresentation
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(E : Type*) [NormedAddCommGroup E] [InnerProductSpace ℝ E] [FiniteDimensional ℝ E]
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[Fintype ι]
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(v : OrthonormalBasis ι ℝ E)
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: InnerProductSpace.canonicalCovariantTensor E = ∑ i, (v i) ⊗ₜ[ℝ] (v i) := by
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(v : OrthonormalBasis ι ℝ E) :
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InnerProductSpace.canonicalCovariantTensor E = ∑ i, (v i) ⊗ₜ[ℝ] (v i) := by
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let w := stdOrthonormalBasis ℝ E
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conv =>
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@ -1,5 +1,13 @@
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import Mathlib.Analysis.SpecialFunctions.Integrals
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import Mathlib.Analysis.SpecialFunctions.Log.NegMulLog
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import Mathlib.Analysis.Convex.SpecificFunctions.Deriv
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import Nevanlinna.analyticAt
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open scoped Interval Topology
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open Real Filter MeasureTheory intervalIntegral
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structure Divisor where
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toFun : ℂ → ℤ
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@ -48,10 +56,10 @@ theorem Divisor.support_cap_compact
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exact Set.inter_subset_right
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noncomputable def AnalyticOn.zeroDivisor
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noncomputable def AnalyticOnNhd.zeroDivisor
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{f : ℂ → ℂ}
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{U : Set ℂ}
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(hf : AnalyticOn ℂ f U) :
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(hf : AnalyticOnNhd ℂ f U) :
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Divisor where
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toFun := by
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@ -124,28 +132,28 @@ noncomputable def AnalyticOn.zeroDivisor
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tauto
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theorem AnalyticOn.support_of_zeroDivisor
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theorem AnalyticOnNhd.support_of_zeroDivisor
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{f : ℂ → ℂ}
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{U : Set ℂ}
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(hf : AnalyticOn ℂ f U) :
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(hf : AnalyticOnNhd ℂ f U) :
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Function.support hf.zeroDivisor ⊆ U := by
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intro z
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contrapose
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intro hz
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dsimp [AnalyticOn.zeroDivisor]
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dsimp [AnalyticOnNhd.zeroDivisor]
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simp
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tauto
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theorem AnalyticOn.support_of_zeroDivisor₂
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theorem AnalyticOnNhd.support_of_zeroDivisor₂
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{f : ℂ → ℂ}
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{U : Set ℂ}
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(hf : AnalyticOn ℂ f U) :
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(hf : AnalyticOnNhd ℂ f U) :
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Function.support hf.zeroDivisor ⊆ f⁻¹' {0} := by
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intro z hz
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dsimp [AnalyticOn.zeroDivisor] at hz
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dsimp [AnalyticOnNhd.zeroDivisor] at hz
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have t₀ := hf.support_of_zeroDivisor hz
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simp [hf.support_of_zeroDivisor hz] at hz
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let A := hz.1
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@ -11,7 +11,7 @@ open Real
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theorem jensen_case_R_eq_one
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(f : ℂ → ℂ)
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(h₁f : AnalyticOn ℂ f (Metric.closedBall 0 1))
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(h₁f : AnalyticOnNhd ℂ f (Metric.closedBall 0 1))
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(h₂f : f 0 ≠ 0) :
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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
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@ -24,7 +24,7 @@ theorem jensen_case_R_eq_one
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have h'₂f : ∃ u ∈ (Metric.closedBall (0 : ℂ) 1), f u ≠ 0 := by
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use 0; simp; exact h₂f
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obtain ⟨F, h₁F, h₂F, h₃F⟩ := AnalyticOnCompact.eliminateZeros₂ h₁U h₂U h₁f h'₂f
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obtain ⟨F, h₁F, h₂F, h₃F⟩ := AnalyticOnNhdCompact.eliminateZeros₂ h₁U h₂U h₁f h'₂f
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have h'₁F : ∀ z ∈ Metric.closedBall (0 : ℂ) 1, HolomorphicAt F z := by
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intro z h₁z
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@ -259,9 +259,9 @@ theorem jensen_case_R_eq_one
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intro x ⟨h₁x, _⟩
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simp
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dsimp [AnalyticOn.order] at h₁x
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dsimp [AnalyticOnNhd.order] at h₁x
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simp only [Function.mem_support, ne_eq, Nat.cast_eq_zero, not_or] at h₁x
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exact AnalyticAt.supp_order_toNat (AnalyticOn.order.proof_1 h₁f x) h₁x
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exact AnalyticAt.supp_order_toNat (AnalyticOnNhd.order.proof_1 h₁f x) h₁x
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--
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intro x hx
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@ -297,7 +297,7 @@ theorem jensen
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{R : ℝ}
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(hR : 0 < R)
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(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
|
||||
apply AnalyticOn.comp (t := Metric.closedBall 0 R)
|
||||
have h₁F : AnalyticOnNhd ℂ F (Metric.closedBall 0 1) := by
|
||||
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]
|
||||
|
||||
--
|
||||
|
|
|
|||
|
|
@ -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
|
||||
|
|
|
|||
|
|
@ -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": "",
|
||||
"rev": "c260ed920e2ebd23ef9fc8ca3fd24115e04c18b1",
|
||||
"scope": "leanprover-community",
|
||||
"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,
|
||||
|
|
|
|||
Loading…
Reference in New Issue