Prove2Me

A symmetric sum-of-two-squares product inequality

Proved
WorkbookSource.plus_76133

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

lean-workbooksource-checked

prove that

(a+b+c−3abc)2+(ab+bc+ca−3)2≥8(abc−1)2\left(a+b+c-3abc\right)^2+\left(ab+bc+ca-3\right)^2 \ge 8\left(abc-1\right)^2

for nonnegative reals a,b,ca,b,c

Source: InternLM Lean-Workbook, record lean_workbook_plus_76133 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble
import Mathlib
open Real Nat
Formal statement
theorem WorkbookSource.plus_76133 (a b c : ℝ) (ha : a ≥ 0) (hb : b ≥ 0) (hc : c ≥ 0) : (a + b + c - 3 * a * b * c) ^ 2 + (a * b + b * c + c * a - 3) ^ 2 ≥ 8 * (a * b * c - 1) ^ 2   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_76133; Apache-2.0

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