A product of pair-sum differences at total two

Proved

WorkbookSource.base_958

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

lean-workbooksource-checked

Given $a, b, c \ge 0$ satisfy $a + b + c = 2$ Prove that $(a + b - ab)(b + c - bc)(c + a - ca) \le 1 - abc$

Source: InternLM Lean-Workbook, record lean_workbook_958 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_958 (a b c : ℝ) (ha : 0 ≤ a) (hb : 0 ≤ b) (hc : 0 ≤ c) (hab : a + b + c = 2) : (a + b - a * b) * (b + c - b * c) * (c + a - c * a) ≤ 1 - a * b * c  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_958; Apache-2.0

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