A product of pairwise corrections at sum three

Proved

WorkbookSource.base_16097

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

lean-workbooksource-checked

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

Source: InternLM Lean-Workbook, record lean_workbook_16097 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_16097 (a b c : ℝ) (ha : a + b + c = 3) : (a + b - a * b) * (b + c - b * c) * (c + a - c * a) + a * b * c ≤ 9 / 4  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_16097; Apache-2.0

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