lean_workbook_plus_25015

Proved

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

Let $a,b,c$ be positive real numbers . Prove that $\frac{a^2}{a+b}+\frac{b^2}{b+c}+\frac{c^2}{c+a}\ge \frac{a+b+c}{2}.$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_25015 : ∀ a b c : ℝ, a > 0 ∧ b > 0 ∧ c > 0 → a^2 / (a + b) + b^2 / (b + c) + c^2 / (c + a) ≥ (a + b + c) / 2   :=  by sorry

Source

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

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