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theorem proved tactic proof

phi_lt_onePointSixOneNine

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formal statement (Lean)

  93theorem phi_lt_onePointSixOneNine : φ < (1.619 : ℝ) := by

proof body

Tactic-mode proof.

  94  simp only [φ]
  95  have h5 : Real.sqrt 5 < (2.238 : ℝ) := by
  96    have h : (5 : ℝ) < (2.238 : ℝ)^2 := by norm_num
  97    rw [← Real.sqrt_sq (by norm_num : (0 : ℝ) ≤ 2.238)]
  98    exact Real.sqrt_lt_sqrt (by norm_num) h
  99  linarith
 100
 101/-- φ < 1.8. -/

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