A linear term and triple product are at most two

Proved

WorkbookSource.base_48726

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

lean-workbooksource-checked

Let $a,$ $b$ and $c$ are non-negative numbers such that $a+b+c=2.$ Prove that $a + 4abc\leq2$

Source: InternLM Lean-Workbook, record lean_workbook_48726 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_48726 (a b c : ℝ) (ha : 0 ≤ a) (hb : 0 ≤ b) (hc : 0 ≤ c) (habc : a + b + c = 2) : a + 4 * a * b * c ≤ 2  :=  by sorry

Source