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theorem proved tactic proof

phi_lt_two

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formal statement (Lean)

  73theorem phi_lt_two : φ < 2 := by

proof body

Tactic-mode proof.

  74  simp only [φ]
  75  have h5 : Real.sqrt 5 < 3 := by
  76    have h9 : (5 : ℝ) < 9 := by norm_num
  77    have hsqrt9 : Real.sqrt 9 = 3 := by
  78      rw [show (9 : ℝ) = 3^2 by norm_num, Real.sqrt_sq (by norm_num : (3 : ℝ) ≥ 0)]
  79    calc Real.sqrt 5 < Real.sqrt 9 := Real.sqrt_lt_sqrt (by norm_num) h9
  80      _ = 3 := hsqrt9
  81  linarith
  82
  83/-- φ > 1.618. -/

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