`phi_gt_161`

proved

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module: IndisputableMonolith.Numerics.Interval.Tactic
domain: Numerics
line: 69 · github
papers citing: none yet

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IndisputableMonolith.Numerics.Interval.Tactic on GitHub at line 69.

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formal source

  66  exact lt_of_le_of_lt h.2 h1
  67
  68/-- Example: Prove φ > 1.61 (using interval lo = 1618/1000) -/
  69theorem phi_gt_161 : (1.61 : ℝ) < (1 + Real.sqrt 5) / 2 := by
  70  have h := phi_in_phiInterval
  71  -- phiInterval.lo = 1618/1000 > 1.61
  72  have h1 : (1.61 : ℝ) < (1618 / 1000 : ℚ) := by norm_num
  73  exact lt_of_lt_of_le h1 h.1
  74
  75/-- Example: Prove φ < 1.62 (using interval hi = 1619/1000) -/
  76theorem phi_lt_162 : (1 + Real.sqrt 5) / 2 < (1.62 : ℝ) := by
  77  have h := phi_in_phiInterval
  78  -- phiInterval.hi = 1619/1000 < 1.62
  79  have h1 : ((1619 / 1000 : ℚ) : ℝ) < (1.62 : ℝ) := by norm_num
  80  exact lt_of_le_of_lt h.2 h1
  81
  82end IndisputableMonolith.Numerics.Interval

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