lean_workbook_plus_82069

Proved

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

FOR $X$ ≥ $1$ , $Y$ ≥ $1$ , PROVE THAT $X+Y+1/(XY)$ ≤ $1/X+1/Y+XY$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_82069 (x y : ℝ) (hx : 1 ≤ x) (hy : 1 ≤ y) (hxy : 0 < x ∧ 0 < y) : x + y + 1/(x*y) ≤ 1/x + 1/y + x*y   :=  by sorry

Source