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    "content": "          (t := {\u03c1 : {\u03c1 // IsNontrivialZero \u03c1} | dyadClass X \u03c1 = j \u2227 X < |(\u03c1 : \u2102).im|})\n          (fun \u03c1 h\u03c1 => h\u03c1.1)).toFinset,\n        (1 / ((2 : \u211d) ^ j * X) ^ 2) * (zeroMult (\u03c1 : \u2102) : \u211d) := by\n        apply Finset.sum_le_sum\n        intro \u03c1 h\u03c1\n        rw [Set.Finite.mem_toFinset] at h\u03c1\n        obtain \u27e8h\u03c1j, hgt\u27e9 := h\u03c1\n        have hlo : (2 : \u211d) ^ j * X \u2264 |(\u03c1 : \u2102).im| := by\n          have h := dyadClass_lower hX0 (show X \u2264 |(\u03c1 : \u2102).im| from hgt.le)\n          rw [h\u03c1j] at h\n          exact h\n        have hlo2 : ((2 : \u211d) ^ j * X) ^ 2 \u2264 ((\u03c1 : \u2102).im) ^ 2 := by\n          have h := pow_le_pow_left\u2080 (by positivity : (0 : \u211d) \u2264 (2 : \u211d) ^ j * X) hlo 2\n          rwa [sq_abs] at h\n        have hsq : ((2 : \u211d) ^ j * X) ^ 2 \u2264 1 + ((\u03c1 : \u2102).im) ^ 2 := by\n          linarith [hlo2, sq_nonneg (\u03c1 : \u2102).im]\n        have hpos1 : (0 : \u211d) < 1 + ((\u03c1 : \u2102).im) ^ 2 := by positivity\n        have hpos2 : (0 : \u211d) < ((2 : \u211d) ^ j * X) ^ 2 := by positivity\n        rw [tailTerm, if_pos hgt]\n        rw [show (zeroMult (\u03c1 : \u2102) : \u211d) / (1 + ((\u03c1 : \u2102).im) ^ 2)\n            = (zeroMult (\u03c1 : \u2102) : \u211d) * (1 / (1 + ((\u03c1 : \u2102).im) ^ 2)) from by ring]\n        rw [show (1 / ((2 : \u211d) ^ j * X) ^ 2) * (zeroMult (\u03c1 : \u2102) : \u211d)\n            = (zeroMult (\u03c1 : \u2102) : \u211d) * (1 / ((2 : \u211d) ^ j * X) ^ 2) from by ring]\n        apply mul_le_mul_of_nonneg_left _ (Nat.cast_nonneg _)\n        rw [div_le_div_iff\u2080 hpos1 hpos2]\n        nlinarith [hsq]\n    _ = (1 / ((2 : \u211d) ^ j * X) ^ 2) *\n          \u2211 \u03c1 \u2208 (Set.Finite.subset (dyadClass_fiber_finite hX0 j)\n            (t := {\u03c1 : {\u03c1 // IsNontrivialZero \u03c1} | dyadClass X \u03c1 = j \u2227 X < |(\u03c1 : \u2102).im|})\n            (fun \u03c1 h\u03c1 => h\u03c1.1)).toFinset, (zeroMult (\u03c1 : \u2102) : \u211d) := by",
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