A product of quadratic sums bounds three cubes

Proved

WorkbookSource.base_33592

by wamlart · Sep 12, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

Let $a,b,c \in R$ . Prove that: $3(a^2+b^2)(b^2+c^2)(c^2+a^2)\geq (ab+bc)^3+(bc+ca)^3+(ca+ab)^3$

Source: InternLM Lean-Workbook, record lean_workbook_33592 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_33592 (a b c : ℝ) : 3 * (a ^ 2 + b ^ 2) * (b ^ 2 + c ^ 2) * (c ^ 2 + a ^ 2) ≥ (a * b + b * c) ^ 3 + (b * c + c * a) ^ 3 + (c * a + a * b) ^ 3  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_33592; Apache-2.0

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