Three quadratic factors bound a cubed pairwise sum

Proved

WorkbookSource.base_28463

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

lean-workbooksource-checked

Prove that $(a^2+2bc)(b^2+2ac)(c^2+2ab)\geq(ab+ac+bc)^3$ for $a\geq0, b\geq0, c\geq0$ .

Source: InternLM Lean-Workbook, record lean_workbook_28463 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_28463 (a b c : ℝ) (ha : a ≥ 0) (hb : b ≥ 0) (hc : c ≥ 0) : (a^2 + 2 * b * c) * (b^2 + 2 * a * c) * (c^2 + 2 * a * b) ≥ (a * b + a * c + b * c)^3  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_28463; Apache-2.0

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