A cubic bound under a weighted nonnegative sum constraint

Proved

WorkbookSource.base_14631

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

lean-workbooksource-checked

Let $a,b,c\ge 0$ and $a+2b+c=6$ Prove that

a+ab+abc\leq 9

Source: InternLM Lean-Workbook, record lean_workbook_14631 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_14631 (a b c: ℝ) (ha : 0 ≤ a) (hb : 0 ≤ b) (hc : 0 ≤ c) (h : a + 2 * b + c = 6) : a + a * b + a * b * c ≤ 9  :=  by sorry

Source