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theorem proved term proof

path_length_log_growth

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formal statement (Lean)

  74theorem path_length_log_growth {N M : ℝ} (hN : 1 < N) (hM : N < M) :
  75    avgPathLength N < avgPathLength M := by

proof body

Term-mode proof.

  76  unfold avgPathLength
  77  have h_log_phi_pos : 0 < Real.log phi := Real.log_pos one_lt_phi
  78  apply (div_lt_div_iff_of_pos_right h_log_phi_pos).mpr
  79  exact Real.log_lt_log (by linarith) hM
  80
  81/-! ## §3. Clustering ratio -/
  82
  83/-- Predicted clustering ratio (RS / Erdős-Rényi baseline). -/

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