Prove2Me

A sixth-degree inequality involving squared differences

Proved
WorkbookSource.plus_27702

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

lean-workbooksource-checked

If a,b,ca,b,c are non-negative numbers, such that ab+bc+ca>0ab+bc+ca>0 . then prove: 2∑(a−b)2(a+b−c)2(b+c)(c+a)≥3(a−b)2(b−c)2(c−a)22\sum(a-b)^2(a+b-c)^2(b+c)(c+a)\geq 3(a-b)^2(b-c)^2(c-a)^2

Source: InternLM Lean-Workbook, record lean_workbook_plus_27702 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble
import Mathlib
open Real Nat
Formal statement
theorem WorkbookSource.plus_27702 (a b c : ℝ) (ha : a ≥ 0) (hb : b ≥ 0) (hc : c ≥ 0) (hab : a * b + b * c + c * a > 0) : 2 * ((a - b) ^ 2 * (a + b - c) ^ 2 * (b + c) * (c + a) + (b - c) ^ 2 * (b + c - a) ^ 2 * (c + a) * (a + b) + (c - a) ^ 2 * (c + a - b) ^ 2 * (a + b) * (b + c)) ≥ 3 * ((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_27702; Apache-2.0

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