lean_workbook_plus_13549

Proved

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

Let $x \geq y \geq z$ be real numbers such that $xy + yz + zx = 1$ . Prove that $xz < \frac 12.$ Is it possible to improve the value of constant $\frac 12 \ ?$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_13549 (x y z : ℝ) (hxy : x ≥ y ∧ y ≥ z) (h : x * y + y * z + z * x = 1) : x * z < 1 / 2   :=  by sorry

Source

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

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