A mixed linear, quadratic and cubic expression is at most eighteen

Proved

WorkbookSource.base_40402

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

lean-workbooksource-checked

Let $a,b,c\geq 0, a+b+c=5 .$

2a+2ab+abc\le 18.

Source: InternLM Lean-Workbook, record lean_workbook_40402 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_40402 (a b c : ℝ) (ha : 0 ≤ a) (hb : 0 ≤ b) (hc : 0 ≤ c) (hab : a + b + c = 5) : 2 * a + 2 * a * b + a * b * c ≤ 18  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_40402; Apache-2.0

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