A squared cyclic cubic sum bounds symmetric products

Proved

WorkbookSource.base_10113

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

lean-workbooksource-checked

Prove that for positive reals a, b, and c, the following inequality holds:

$(a^2b+b^2c+c^2a)^2\geq abc(a+b+c)(ab+ac+bc)$

Source: InternLM Lean-Workbook, record lean_workbook_10113 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_10113 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a^2 * b + b^2 * c + c^2 * a)^2 ≥ a * b * c * (a + b + c) * (a * b + b * c + c * a)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_10113; Apache-2.0

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