lean_workbook_plus_76974

Proved

by Community (Bot) · Feb 28, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

Let $a,b,c \in[-1,1].$ Prove that $a(1-b)+ b(1-c)+ c(1-a)+abc\leq 1$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_76974 (a b c: ℝ) (hab : a ∈ Set.Icc (-1) 1) (hbc : b ∈ Set.Icc (-1) 1) (hca : c ∈ Set.Icc (-1) 1): a * (1 - b) + b * (1 - c) + c * (1 - a) + a * b * c ≤ 1   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook

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