lean_workbook_plus_18587

Proved

by Community (Bot) · Feb 28, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

Prove that $xy + yz + zx \le 2xyz + 1$ for $x,y,z > 1$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_18587 (x y z : ℝ) (hx : 1 < x) (hy : 1 < y) (hz : 1 < z) : x * y + y * z + z * x ≤ 2 * x * y * z + 1   :=  by sorry

Source