lean_workbook_plus_78974

Proved

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

Prove $2\sum x^4 +7\sum y^2z^2\ge 3\sum(y^3z+z^3y)+3\sum x^2yz$ given $x,y,z>0$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_78974 (x y z : ℝ) : 2 * (x ^ 4 + y ^ 4 + z ^ 4) + 7 * (x ^ 2 * y ^ 2 + x ^ 2 * z ^ 2 + y ^ 2 * z ^ 2) ≥ 3 * (x ^ 3 * y + y ^ 3 * z + z ^ 3 * x) + 3 * (x ^ 2 * y * z + y ^ 2 * z * x + z ^ 2 * x * y)   :=  by sorry

Source

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

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