A product of quadratic differences at fixed sum three

Proved

WorkbookSource.base_38914

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

lean-workbooksource-checked

Let $a,b,c \geq 0$ with $a+b+c=3$ ,prove that: $(b^{2}-bc+c^{2}) (c^{2}-ca+a^{2}) (a^{2}-ab+b^{2})\geq abc.$

Source: InternLM Lean-Workbook, record lean_workbook_38914 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_38914 (a b c : ℝ) (ha : a ≥ 0) (hb : b ≥ 0) (hc : c ≥ 0) (hab : a + b + c = 3) : (b^2 - b * c + c^2) * (c^2 - c * a + a^2) * (a^2 - a * b + b^2) ≥ a * b * c  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_38914; Apache-2.0

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