A cubed symmetric quadratic sum bounds two cyclic cubic sums

Proved

WorkbookSource.base_41707

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

lean-workbooksource-checked

Let $a,b,c$ be positive real numbers. Prove that: $(a^2+b^2+c^2+ab+bc+ca)^3 \ge 24(a^2b+b^2c+c^2a)(b^2a+c^2b+a^2c)$

Source: InternLM Lean-Workbook, record lean_workbook_41707 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_41707 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a^2 + b^2 + c^2 + a * b + b * c + c * a)^3 ≥ 24 * (a^2 * b + b^2 * c + c^2 * a) * (b^2 * a + c^2 * b + a^2 * c)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_41707; Apache-2.0

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