A cubic pairwise sum is bounded by quadratic factors

Proved

WorkbookSource.base_29861

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

lean-workbooksource-checked

For $a, b, c > 0$ real numbers, prove that: $(2a^2+bc)(2b^2+ac)(2c^2+ab) \ge (ab+bc+ca)^3$

Source: InternLM Lean-Workbook, record lean_workbook_29861 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_29861 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (2 * a ^ 2 + b * c) * (2 * b ^ 2 + a * c) * (2 * c ^ 2 + a * b) ≥ (a * b + b * c + c * a) ^ 3  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_29861; Apache-2.0

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