A normalized product lower bound with cubic corrections

Proved

WorkbookSource.base_10232

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

lean-workbooksource-checked

Let $a,b,c$ be non-negative real numbers such that $a+b+c=3$ . Prove that:

(a^2 + b^2 + c ^2+abc-3) (2 +abc) \geq 3

Source: InternLM Lean-Workbook, record lean_workbook_10232 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_10232 (a b c : ℝ) (ha : a ≥ 0) (hb : b ≥ 0) (hc : c ≥ 0) (hab : a + b + c = 3) :  (a^2 + b^2 + c^2 + a * b * c - 3) * (2 + a * b * c) ≥ 3  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_10232; Apache-2.0

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