lean_workbook_plus_13317

Proved

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

If $x,y,z$ are positive real numbers such that $3=xy+yz+zx$ show that $3(x+y)(x+z)(y+z)(x+y+z)\ge 2(x^2+y^2+z^2+6)$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_13317 (x y z : ℝ) (h : 3 = x * y + y * z + z * x) : 3 * (x + y) * (x + z) * (y + z) * (x + y + z) ≥ 2 * (x ^ 2 + y ^ 2 + z ^ 2 + 6)   :=  by sorry

Source

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

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