lean_workbook_plus_3882

Proved

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

Let $a, b$ and $c$ be be positive real numbers such that $a+b+c=2$ . Prove that $(a-1) (b-1) (c-1) (1-abc)\ge \frac{2375a^4b^4c^4}{512}.$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_3882 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (habc : a * b * c = 1) (hab : a + b + c = 2) :  (a - 1) * (b - 1) * (c - 1) * (1 - a * b * c) ≥ (2375 * a ^ 4 * b ^ 4 * c ^ 4) / 512   :=  by sorry

Source

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

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