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lemma proved tactic proof

phi_sq_eq

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formal statement (Lean)

  70lemma phi_sq_eq : phi^2 = phi + 1 := by

proof body

Tactic-mode proof.

  71  simp only [phi]
  72  have h5_pos : (0 : ℝ) ≤ 5 := by norm_num
  73  have hsq : (Real.sqrt 5)^2 = 5 := Real.sq_sqrt h5_pos
  74  ring_nf
  75  linear_combination (1/4) * hsq
  76
  77/-- Tighter lower bound: φ > 1.5 (since √5 > 2, so (1 + √5)/2 > 1.5). -/

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