lean_workbook_plus_43466

Proved

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

Prove that if $a\geq b\geq c > 0$ and $a+b+c = 1$ , then $\frac{b}{b+c}+\frac{c}{c+a}+\frac{a}{a+b} \ge \frac{3}{2}$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_43466 (a b c : ℝ) (h1 : a ≥ b ∧ b ≥ c ∧ c > 0 ∧ a + b + c = 1) :
  b / (b + c) + c / (c + a) + a / (a + b) ≥ 3 / 2   :=  by sorry

Source

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

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