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theorem proved tactic proof

phi10_fibonacci

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formal statement (Lean)

  29theorem phi10_fibonacci : phi ^ 10 = 55 * phi + 34 := by

proof body

Tactic-mode proof.

  30  have h2 := phi_sq_eq
  31  have h3 : phi ^ 3 = 2 * phi + 1 := by nlinarith
  32  have h4 : phi ^ 4 = 3 * phi + 2 := by nlinarith
  33  have h5 : phi ^ 5 = 5 * phi + 3 := by nlinarith
  34  have h10 : phi ^ 10 = phi ^ 5 * phi ^ 5 := by ring
  35  rw [h10]; nlinarith
  36
  37/-- φ^10 > 100. -/

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