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theorem proved tactic proof

no_strip_zeros_of_decomposed_data

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formal statement (Lean)

  44theorem no_strip_zeros_of_decomposed_data (data : RSPhysicalThesisData) :
  45    ∀ ρ : ℂ, riemannZeta ρ = 0 → 1 / 2 < ρ.re → ρ.re < 1 → False := by

proof body

Tactic-mode proof.

  46  intro ρ _hzero hlo hhi
  47  let sensor : DefectSensor := zetaDefectSensor ρ.re ⟨hlo, hhi⟩ 1
  48  have hm : sensor.charge ≠ 0 := by
  49    dsimp [sensor]
  50    exact zetaDefectSensor_charge_ne_zero ρ.re ⟨hlo, hhi⟩
  51  have hdiv : CostDivergent sensor :=
  52    nonzero_charge_cost_divergent sensor hm
  53  exact no_cost_divergent_sensor_of_boundary_transport data.boundaryTransport sensor hdiv
  54
  55/-- If no strip zero exists, the old `RSPhysicalThesis` holds vacuously. -/

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