An upper bound for a product of quadratic expressions

Proved

WorkbookSource.base_4528

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

lean-workbooksource-checked

Prove that: $(a^{2}+a+1)(b^{2}+b+1)(c^{2}+c+1) \leq 27$ where $a;b;c$ are non-negative and satisfying $a+b+c=3$

Source: InternLM Lean-Workbook, record lean_workbook_4528 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_4528 (a b c : ℝ) (ha : 0 ≤ a) (hb : 0 ≤ b) (hc : 0 ≤ c) (hab : a + b + c = 3) : (a^2 + a + 1) * (b^2 + b + 1) * (c^2 + c + 1) ≤ 27  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_4528; Apache-2.0

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