Prove2Me

An eighth-degree inequality involving squared pairwise differences

Proved
WorkbookSource.plus_3237

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

lean-workbooksource-checked

For non-negative numbers a,b,ca, b, c, prove that 3∑(a−b)2(a+b−c)2(a2+ac+c2)(b2+bc+c2)≥4(a+b+c)2(a−b)2(b−c)2(c−a)23\sum (a-b)^2(a+b-c)^2(a^2+ac+c^2)(b^2+bc+c^2) \geq 4 (a+b+c)^2(a-b)^2(b-c)^2(c-a)^2.

Source: InternLM Lean-Workbook, record lean_workbook_plus_3237 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble
import Mathlib
open Real Nat
Formal statement
theorem WorkbookSource.plus_3237 (a b c : ℝ) (ha : 0 ≤ a) (hb : 0 ≤ b) (hc : 0 ≤ c) : 3 * ((a - b) ^ 2 * (a + b - c) ^ 2 * (a ^ 2 + a * c + c ^ 2) * (b ^ 2 + b * c + c ^ 2) + (b - c) ^ 2 * (b + c - a) ^ 2 * (b ^ 2 + b * a + a ^ 2) * (c ^ 2 + c * a + a ^ 2) + (c - a) ^ 2 * (c + a - b) ^ 2 * (c ^ 2 + c * b + b ^ 2) * (a ^ 2 + a * b + b ^ 2)) ≥ 4 * (a + b + c) ^ 2 * (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_plus_3237; Apache-2.0

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