lean_workbook_plus_76609

Proved

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

Let $a, b$ and $c$ be positive real numbers. Prove that

\big(\frac{a}{b+c}+\frac{1}{2}\big) \big(\frac{b}{c+a}+\frac{1}{2}\big) \big(\frac{c}{a+b}+\frac{1}{2}\big)\ge 1

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_76609 (a b c : ℝ) (ha : a > 0) (hb : b > 0) (hc : c > 0) : (a / (b + c) + 1 / 2) * (b / (c + a) + 1 / 2) * (c / (a + b) + 1 / 2) ≥ 1   :=  by sorry

Source

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

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