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@ -394,7 +394,13 @@ lemma int₄
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have h₁a : a / R ∈ Metric.closedBall 0 1 := by
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simp
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simp at ha
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sorry
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rw [div_le_comm₀]
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simp
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have : R = |R| := by
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exact Eq.symm (abs_of_pos hR)
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rwa [this] at ha
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rwa [abs_of_pos hR]
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simp
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have t₀ {x : ℝ} : circleMap 0 R x = R * circleMap 0 1 x := by
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unfold circleMap
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@ -304,16 +304,17 @@ theorem jensen
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simp at hs
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simp [hs.1]
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rw [finsum_eq_sum_of_support_subset _ h₁G'] at decompose_int_G
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have : ∑ s ∈ h₃f.toFinset, (h₁f.meromorphicOn.divisor s) * ∫ (x_1 : ℝ) in (0)..(2 * π), log ‖circleMap 0 R x_1 - s‖ = 0 := by
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apply Finset.sum_eq_zero
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intro x hx
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rw [int₃ _]
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simp
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simp at hx
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let ZZ := h₁f.meromorphicOn.divisor.supportInU
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simp at ZZ
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let UU := ZZ x hx
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simpa
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have : ∑ s ∈ h₃f.toFinset, (h₁f.meromorphicOn.divisor s) * ∫ (x_1 : ℝ) in (0)..(2 * π), log ‖circleMap 0 R x_1 - s‖ = ∑ s ∈ h₃f.toFinset, (h₁f.meromorphicOn.divisor s) * (2 * π) * log R := by
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apply Finset.sum_congr rfl
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intro s hs
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have : s ∈ Metric.closedBall 0 R := by
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let A := h₁f.meromorphicOn.divisor.supportInU
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have : s ∈ Function.support h₁f.meromorphicOn.divisor := by
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simp at hs
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exact hs
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exact A this
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rw [int₄ hR this]
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linarith
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rw [this] at decompose_int_G
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@ -324,20 +325,42 @@ theorem jensen
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let X := h₄F
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nth_rw 1 [h₄F]
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simp
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have {l : ℝ} : π⁻¹ * 2⁻¹ * (2 * π * l) = l := by
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calc π⁻¹ * 2⁻¹ * (2 * π * l)
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_ = π⁻¹ * (2⁻¹ * 2) * π * l := by ring
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_ = π⁻¹ * π * l := by ring
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_ = (π⁻¹ * π) * l := by ring
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_ = 1 * l := by
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have : π⁻¹ * 2⁻¹ * (2 * π) = 1 := by
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calc π⁻¹ * 2⁻¹ * (2 * π)
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_ = π⁻¹ * (2⁻¹ * 2) * π := by ring
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_ = π⁻¹ * π := by ring
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_ = (π⁻¹ * π) := by ring
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_ = 1 := by
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rw [inv_mul_cancel₀]
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exact pi_ne_zero
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_ = l := by simp
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rw [this]
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--rw [this]
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rw [log_mul]
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rw [log_prod]
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simp
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rw [add_comm]
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rw [mul_add]
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rw [← mul_assoc (π⁻¹ * 2⁻¹), this]
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simp
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rw [add_comm]
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nth_rw 2 [add_comm]
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rw [add_assoc]
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congr
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rw [Finset.mul_sum]
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rw [← sub_eq_add_neg]
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rw [← Finset.sum_sub_distrib]
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rw [Finset.sum_congr rfl]
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intro s hs
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rw [log_mul, log_inv]
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rw [← mul_assoc (π⁻¹ * 2⁻¹)]
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rw [mul_comm _ (2 * π)]
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rw [← mul_assoc (π⁻¹ * 2⁻¹)]
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rw [this]
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simp
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rw [mul_add]
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ring
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--
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--
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intro x hx
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simp at hx
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@ -5,7 +5,7 @@
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"type": "git",
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"subDir": null,
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"scope": "",
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"rev": "134c6ee3da5185da90b69d05697c85bfba57e82e",
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"rev": "a69e6fafa9665613ef0e905036e4d607b75769e0",
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"name": "mathlib",
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"manifestFile": "lake-manifest.json",
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"inputRev": null,
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@ -75,7 +75,7 @@
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"type": "git",
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"subDir": null,
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"scope": "leanprover-community",
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"rev": "7805acf1864ba1a2e359f86a8f092ccf1438ad83",
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"rev": "c016aa9938c4cedc9b7066099f99bcae1b1af625",
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"name": "batteries",
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"manifestFile": "lake-manifest.json",
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"inputRev": "main",
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