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theorem proved tactic proof

gamma_unique

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formal statement (Lean)

  52theorem gamma_unique {x : ℝ} (hx : 2 < x) (h : (x - 1) * (x - 2) = 2) :
  53    x = gamma := by

proof body

Tactic-mode proof.

  54  -- (x-1)(x-2) = x^2 - 3x + 2 = 2 ⇒ x^2 - 3x = 0 ⇒ x(x-3) = 0.
  55  -- Solutions: x = 0 or x = 3. With x > 2, forced x = 3 = gamma.
  56  have h_factored : x * (x - 3) = 0 := by nlinarith
  57  rcases mul_eq_zero.mp h_factored with h0 | h3
  58  · linarith
  59  · unfold gamma; linarith
  60
  61/-! ## §2. Small-world path-length scaling -/
  62
  63/-- Predicted average path length: `L(N) = log_φ N`. -/

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