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theorem proved tactic proof

phi5_bounds

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formal statement (Lean)

  47theorem phi5_bounds : 10 < phi ^ 5 ∧ phi ^ 5 < 12 := by

proof body

Tactic-mode proof.

  48  have hphi_lo : (1.61 : ℝ) < phi := phi_gt_onePointSixOne
  49  have hphi_hi : phi < (1.62 : ℝ) := phi_lt_onePointSixTwo
  50  constructor
  51  · calc (10 : ℝ) < (1.61 : ℝ)^5 := by norm_num
  52      _ < phi^5 := pow_lt_pow_left₀ hphi_lo (by norm_num) (by norm_num)
  53  · calc phi^5 < (1.62 : ℝ)^5 := pow_lt_pow_left₀ hphi_hi (le_of_lt phi_pos) (by norm_num)
  54      _ < 12 := by norm_num
  55
  56/-- String tension is in (0.08, 0.11): derived from φ^5 ∈ (10, 12). -/

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