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theorem proved tactic proof

J_phi_pos

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formal statement (Lean)

  41theorem J_phi_pos : J phi > 0 := by

proof body

Tactic-mode proof.

  42  unfold J
  43  have h_phi_sq : phi ^ 2 = phi + 1 := Constants.phi_sq_eq
  44  have h_phi_pos : 0 < phi := Constants.phi_pos
  45  have h_phi_inv : phi⁻¹ = phi - 1 := by
  46    have h : phi * (phi - 1) = 1 := by nlinarith [h_phi_sq]
  47    field_simp; linarith
  48  rw [h_phi_inv]
  49  linarith [Constants.phi_gt_onePointFive]
  50

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