A pairwise-product correction bound at sum three

Proved

WorkbookSource.plus_21359

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

lean-workbooksource-checked

Let $a,b,c$ are nonnegative real numbers such that $a+b+c=3.$ ab(1-c)+bc(1-a)+ca(1-b)\leq\frac{9}{4}.$

Source: InternLM Lean-Workbook, record lean_workbook_plus_21359 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_21359 (a b c : ℝ) (ha : 0 ≤ a) (hb : 0 ≤ b) (hc : 0 ≤ c) (hab : a + b + c = 3) : a * b * (1 - c) + b * c * (1 - a) + c * a * (1 - b) ≤ 9 / 4   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_21359; Apache-2.0

View graph