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theorem proved tactic proof

BIT_carrier_period_band

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formal statement (Lean)

  95theorem BIT_carrier_period_band :
  96    0.12 < BIT_carrier_period ∧ BIT_carrier_period < 0.13 := by

proof body

Tactic-mode proof.

  97  unfold BIT_carrier_period
  98  have h1 := phi_gt_onePointSixOne
  99  have h2 := phi_lt_onePointSixTwo
 100  have h_pos : (0 : ℝ) < 5 * phi := by positivity
 101  refine ⟨?_, ?_⟩
 102  · -- 0.12 < 1 / (5 * phi)
 103    rw [lt_div_iff₀ h_pos]
 104    -- 0.12 * (5 * phi) < 1
 105    -- = 0.6 * phi < 1
 106    nlinarith
 107  · -- 1 / (5 * phi) < 0.13
 108    rw [div_lt_iff₀ h_pos]
 109    -- 1 < 0.13 * (5 * phi)
 110    -- = 0.65 * phi
 111    nlinarith
 112
 113/-! ## §2. FRB amplification factor: 360 = 8 · 45 -/
 114
 115/-- Canonical FRB per-rung amplification: 8 × 45 = 360 (8-tick
 116window × consciousness-gap). -/

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