A fifth-degree bound involving three pairwise sums

Proved

WorkbookSource.base_4786

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

lean-workbooksource-checked

Prove that for all $a,b,c \ge 0$ we have : $(a+b+c)^2\left(a+b\right)\left(a+c\right)\left(b+c\right) \ge 24abc \left(a^2+b^2+c^2\right)$

Source: InternLM Lean-Workbook, record lean_workbook_4786 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_4786 (a b c : ℝ) (ha : 0 ≤ a) (hb : 0 ≤ b) (hc : 0 ≤ c) : (a + b + c) ^ 2 * (a + b) * (a + c) * (b + c) ≥ 24 * a * b * c * (a ^ 2 + b ^ 2 + c ^ 2)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_4786; Apache-2.0

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