Three squared pairwise factors bound a cubed pairwise sum

Proved

WorkbookSource.plus_60799

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

lean-workbooksource-checked

For a,b,c≥0,prove the ineq: $27(a^2 + b^2)(b^2 + c^2)(c^2 + a^2)$ ≥ $8(ab + bc + ca)^3$

Source: InternLM Lean-Workbook, record lean_workbook_plus_60799 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_60799 (a b c : ℝ) (ha : 0 ≤ a) (hb : 0 ≤ b) (hc : 0 ≤ c) : 27 * (a^2 + b^2) * (b^2 + c^2) * (c^2 + a^2) ≥ 8 * (a * b + b * c + c * a)^3   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_60799; Apache-2.0

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