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theorem proved tactic proof

lambdaRS_band

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formal statement (Lean)

  41theorem lambdaRS_band : (1.88 : ℝ) < lambdaRS ∧ lambdaRS < 2.03 := by

proof body

Tactic-mode proof.

  42  unfold lambdaRS
  43  have h5 : phi ^ 5 = 5 * phi + 3 := phi5_eq
  44  have h1 := phi_gt_onePointSixOne
  45  have h2 := phi_lt_onePointSixTwo
  46  rw [h5]
  47  constructor
  48  · have : 8 * (5 * phi + 3) / 45 > 8 * (5 * 1.61 + 3) / 45 := by
  49      apply div_lt_div_of_pos_right _ (by norm_num)
  50      nlinarith
  51    linarith
  52  · have : 8 * (5 * phi + 3) / 45 < 8 * (5 * 1.62 + 3) / 45 := by
  53      apply div_lt_div_of_pos_right _ (by norm_num)
  54      nlinarith
  55    linarith
  56

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