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theorem proved term proof

phi_not_rational

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formal statement (Lean)

  79theorem phi_not_rational : ∀ q : ℚ, (q : ℝ) ≠ phi := by

proof body

Term-mode proof.

  80  intro q heq
  81  apply phi_irrational
  82  exact Set.mem_range.mpr ⟨q, heq⟩
  83
  84/-- **THEOREM IC-002.6**: The golden ratio satisfies an irreducible quadratic.
  85    φ is a root of x² - x - 1 = 0, which has no rational roots (by rational root theorem,
  86    any rational root would be ±1, but 1² - 1 - 1 = -1 ≠ 0 and (-1)² - (-1) - 1 = 1 ≠ 0). -/

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