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ZetaInvBnd work
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PrimeNumberTheoremAnd/ZetaBounds.lean

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@@ -1730,11 +1730,15 @@ lemma ZetaInvBnd :
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(hσ : σ ∈ Ico (1 - A / (Real.log |t|) ^ 9) 1),
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1 / ‖ζ (σ + t * I)‖ ≤ C * (Real.log |t|) ^ 7 := by
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obtain ⟨A', hA', C', hC', h'⟩ := Zeta_diff_Bnd
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let A := min A' <| (1 / 16 : ℝ)
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obtain ⟨C₂, C₂pos, hC'⟩ := ZetaInvBound2
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let A := min A' <| (1 / 2 : ℝ) * (C' / 2 * C₂) ^ 4
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have Apos : 0 < A := by have := hA'.1; positivity
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let C := C'
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have Cpos : 0 < C := by positivity
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refine ⟨A, ⟨Apos, by norm_num [A]⟩ , C, Cpos, ?_⟩
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have A_le_A' : A ≤ A' := by simp [A]
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let C := C' * A ^ (3 / 4 : ℝ) - 2 * A * C₂
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have Cpos : 0 < C := by
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apply sub_pos.mpr
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sorry
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refine ⟨A, ⟨Apos, by linarith [hA'.2]⟩ , C, Cpos, ?_⟩
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intro σ t t_gt hσ
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have logt_gt_one := logt_gt_one t_gt
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have σ_ge : 1 - A / |t|.log ≤ σ := by

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