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theorem proved term proof

phiInv_lt_phi

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formal statement (Lean)

  41theorem phiInv_lt_phi : phiInv < phi := by

proof body

Term-mode proof.

  42  have h := phi_pos
  43  have hone := one_lt_phi
  44  unfold phiInv
  45  calc 1 / phi < 1 := (div_lt_one h).mpr hone
  46    _ < phi := hone
  47
  48/-- 1/φ = φ - 1 (Fibonacci-phi identity).
  49    Proof: φ·(φ-1) = φ² - φ = (φ+1) - φ = 1, so φ-1 = 1/φ. -/

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