Prove2Me

lean_workbook_plus_77732

Proved

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

Let x,y,zx,y,z be positive real numbers. Prove that xy+yz+zx⩾z(x+y)y(y+z)+x(y+z)z(z+x)+y(z+x)x(x+y).\frac{x}{y}+\frac{y}{z}+\frac{z}{x}\geqslant\frac{z(x+y)}{y(y+z)}+\frac{x(y+z)}{z(z+x)}+\frac{y(z+x)}{x(x+y)}.

Preamble
import Mathlib.Analysis.Complex.Basic
Formal statement
theorem lean_workbook_plus_77732 (x y z : ℝ) (hx : 0 < x) (hy : 0 < y) (hz : 0 < z) : (x / y + y / z + z / x) ≥ (z * (x + y) / (y * (y + z)) + x * (y + z) / (z * (z + x)) + y * (z + x) / (x * (x + y)))   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook

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