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lemma proved tactic proof

phi_eq_one_add_inv_phi

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formal statement (Lean)

  47lemma phi_eq_one_add_inv_phi : phi = 1 + (1 : ℝ) / phi := by

proof body

Tactic-mode proof.

  48  have hne : phi ≠ 0 := phi_ne_zero
  49  calc
  50    phi = phi ^ 2 / phi := by field_simp [hne]
  51    _ = (phi + 1) / phi := by simp [phi_sq_eq]
  52    _ = 1 + (1 : ℝ) / phi := by field_simp [hne]
  53

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