lean_workbook_plus_18307

import Mathlib.Analysis.Complex.Basic

theorem lean_workbook_plus_18307 : ∀ a b c k : ℝ, a ≥ 0 ∧ b ≥ 0 ∧ c ≥ 0 ∧ a * b + b * c + c * a = 1 ∧ k > 0 → (a * b + k) / (a + b) + (b * c + k) / (b + c) + (c * a + k) / (c + a) ≤ (k - 7) / 2   :=  by sorry