Prove2Me

lean_workbook_plus_31668

Proved

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

If x,y,z are real positive numbers, prove that \n (x+y+z)2(xy+yz+zx)2≤3(y2+yz+z2)(z2+zx+x2)(x2+xy+y2) (x+y+z)^2(xy+yz+zx)^2\leq3(y^2+yz+z^2)(z^2+zx+x^2)(x^2+xy+y^2) \n

Preamble
import Mathlib.Analysis.Complex.Basic
Formal statement
theorem lean_workbook_plus_31668 (x y z : ℝ) (hx : 0 < x) (hy : 0 < y) (hz : 0 < z) : (x + y + z) ^ 2 * (x * y + y * z + z * x) ^ 2 ≤ 3 * (y ^ 2 + y * z + z ^ 2) * (z ^ 2 + z * x + x ^ 2) * (x ^ 2 + x * y + y ^ 2)   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook

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