Prove2Me

A cubed quadratic sum bounds a pairwise product times a cubic sum

Proved
WorkbookSource.base_48485

by wamlart · Sep 13, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

Let x,y,z>0x,y,z>0 show that

8(x2+y2+z2)3≥9(x+y)(y+z)(z+x)(x3+y3+z3)8(x^2+y^2+z^2)^3\ge 9(x+y)(y+z)(z+x)(x^3+y^3+z^3)

Source: InternLM Lean-Workbook, record lean_workbook_48485 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble
import Mathlib
open Real Nat
Formal statement
theorem WorkbookSource.base_48485 (x y z : ℝ) (hx : 0 < x) (hy : 0 < y) (hz : 0 < z) : 8 * (x ^ 2 + y ^ 2 + z ^ 2) ^ 3 ≥ 9 * (x + y) * (y + z) * (z + x) * (x ^ 3 + y ^ 3 + z ^ 3)  :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_48485; Apache-2.0

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