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theorem proved term proof

phi_fixed_point'

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formal statement (Lean)

  27theorem phi_fixed_point' : phi = 1 + phi⁻¹ := by

proof body

Term-mode proof.

  28  have hphi_pos : phi > 0 := phi_pos
  29  have hphi_ne : phi ≠ 0 := ne_of_gt hphi_pos
  30  -- From phi_squared: φ² = φ + 1
  31  -- Divide both sides by φ: φ = 1 + 1/φ
  32  have h := phi_squared
  33  field_simp at h ⊢
  34  linarith
  35
  36/-- φ > 1: The golden ratio is strictly greater than 1.
  37
  38    This is already proven in Constants.lean -/

depends on (7)

Lean names referenced from this declaration's body.