A cubic sum and squared triple product have a fixed lower bound

Proved

WorkbookSource.base_10515

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

lean-workbooksource-checked

Let $a,b,c \geq 0$ and $a+b+c=3$ . Prove that $a^3+b^3+c^3+2a^2b^2c^2 \geq 5$ .

Source: InternLM Lean-Workbook, record lean_workbook_10515 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_10515 (a b c : ℝ) (ha : 0 ≤ a) (hb : 0 ≤ b) (hc : 0 ≤ c) (hab : a + b + c = 3) : a^3 + b^3 + c^3 + 2 * a^2 * b^2 * c^2 ≥ 5  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_10515; Apache-2.0

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