Squared pairwise sums bound mixed quadratic factors

Proved

WorkbookSource.base_37968

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

lean-workbooksource-checked

The following inequality is true too: For non-negative $a,$ $b$ and $c$ prove that:

$4(a^2 + bc)(b^2 + ca)(c^2 + ab) \leq (a + b)^2(b + c)^2(c + a)^2$

Source: InternLM Lean-Workbook, record lean_workbook_37968 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_37968 (a b c : ℝ) (ha : 0 ≤ a) (hb : 0 ≤ b) (hc : 0 ≤ c) : 4 * (a^2 + b * c) * (b^2 + c * a) * (c^2 + a * b) ≤ (a + b)^2 * (b + c)^2 * (c + a)^2  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_37968; Apache-2.0

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