lean_workbook_plus_69140

import Mathlib.Analysis.Complex.Basic

theorem lean_workbook_plus_69140 (a b c : ℝ) (ha : 0 ≤ a) (hb : 0 ≤ b) (hc : 0 ≤ c) (hab : 0 < a + b + c) (h : (a * b) / (c + 1) + (b * c) / (a + 1) + (c * a) / (b + 1) + 2 * (a + b + c) = 6) : a * b + b * c + c * a ≤ 2   :=  by sorry