lean_workbook_plus_33279

Proved

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

If $x,y,z$ are positive numbers with $\frac{x}{y} \ge \frac{1}{2},\frac{y}{z} \ge \frac{1}{2},\frac{z}{x} \ge \frac{1}{2}$ , then \n $xyz \ge (2x-y)(2y-z)(2z-x).$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_33279 (x y z : ℝ) (hx : 0 < x) (hy : 0 < y) (hz : 0 < z) (hxy : x ≥ y / 2) (hyz : y ≥ z / 2) (hzx : z ≥ x / 2) :  x * y * z ≥ (2 * x - y) * (2 * y - z) * (2 * z - x)   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook

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