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theorem proved tactic proof

lambdaRS_band

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formal statement (Lean)

  34theorem lambdaRS_band :
  35    (1.88 : ℝ) < lambdaRS ∧ lambdaRS < 2.03 := by

proof body

Tactic-mode proof.

  36  unfold lambdaRS
  37  have h5 : phi ^ 5 = 5 * phi + 3 := phi5_eq
  38  have h1 := phi_gt_onePointSixOne
  39  have h2 := phi_lt_onePointSixTwo
  40  constructor
  41  · have : 8 * phi ^ 5 / 45 > 8 * (5 * 1.61 + 3) / 45 := by
  42      apply div_lt_div_of_pos_right _ (by norm_num)
  43      nlinarith
  44    linarith
  45  · have : 8 * phi ^ 5 / 45 < 8 * (5 * 1.62 + 3) / 45 := by
  46      apply div_lt_div_of_pos_right _ (by norm_num)
  47      nlinarith
  48    linarith
  49
  50/-- Λ_RS > 0. -/

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depends on (10)

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