A product bound for two cyclic cubic sums

Proved

WorkbookSource.base_374

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

lean-workbooksource-checked

Show that for positive reals $a,b,c$ ,

(a^2b + b^2c + c^2a)(ab^2 + bc^2 + ca^2) \geq 9a^2b^2c^2

Source: InternLM Lean-Workbook, record lean_workbook_374 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_374 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a^2 * b + b^2 * c + c^2 * a) * (a * b^2 + b * c^2 + c * a^2) ≥ 9 * a^2 * b^2 * c^2  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_374; Apache-2.0

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