lean_workbook_plus_41536

Proved

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

Show that $x+\frac{1}{x}-(y+\frac{1}{y}) \geq 0$ for $x \geq y \geq 1$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_41536  (x y : ℝ) (hx : x ≥ 1) (hy : y ≥ 1) (hxy : x ≥ y) :
  x + 1/x - (y + 1/y) ≥ 0   :=  by sorry

Source