A mixed linear-quadratic-cubic upper bound at sum six

Proved

WorkbookSource.base_44260

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

lean-workbooksource-checked

Let $a,b,c\ge 0$ and $a+b+c=6 .$ Prove that

2a+ab+abc\le 18

Source: InternLM Lean-Workbook, record lean_workbook_44260 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_44260 (a b c : ℝ) (ha : 0 ≤ a) (hb : 0 ≤ b) (hc : 0 ≤ c) (habc : a + b + c = 6) : 2*a + a*b + a*b*c ≤ 18  :=  by sorry

Source