Prove2Me

lean_workbook_plus_74676

Proved

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

It's (x+y)(x+z)(y+z)≥89(x+y+z)(xy+xz+yz)(x+y)(x+z)(y+z)\geq\frac{8}{9}(x+y+z)(xy+xz+yz) for positives xx , yy and zz.

Preamble
import Mathlib.Analysis.Complex.Basic
Formal statement
theorem lean_workbook_plus_74676 (x y z : ℝ) (hx : 0 < x) (hy : 0 < y) (hz : 0 < z) : (x + y) * (x + z) * (y + z) ≥ (8 / 9) * (x + y + z) * (x * y + x * z + y * z)   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook

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