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theorem proved tactic proof

phi_squared

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formal statement (Lean)

  13theorem phi_squared : phi ^ 2 = phi + 1 := by

proof body

Tactic-mode proof.

  14  unfold phi
  15  have h5 : (0 : ℝ) ≤ 5 := by norm_num
  16  have hsqrt : Real.sqrt 5 ^ 2 = 5 := Real.sq_sqrt h5
  17  field_simp
  18  ring_nf
  19  rw [hsqrt]
  20  ring
  21
  22/-- φ = 1 + 1/φ: The fixed-point equation.
  23
  24    Proof: From φ² = φ + 1, divide by φ (which is positive) to get φ = 1 + 1/φ
  25    NOTE: Also defined in PhiSupport/Lemmas.lean for use by that module.
  26    Renamed here to avoid conflict. -/

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