lean_workbook_plus_21689

Proved

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

Prove that if $a,b,c>0$ then \n $\frac{1}{2} + \frac{a^2+b^2+c^2}{ab+bc+ca} \geq \frac{a}{b+c} +\frac{b}{c+a} +\frac{c}{a+b} \quad (1)$ \n

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_21689 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (1 / 2 + (a ^ 2 + b ^ 2 + c ^ 2) / (a * b + b * c + c * a) ) ≥ a / (b + c) + b / (c + a) + c / (a + b)   :=  by sorry

Source

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

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