Prove2Me

lean_workbook_plus_15933

Proved

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

Let a,b,c>0. Prove that:

b2+c2b+c+a2+b2a+b+c2+a2c+a≥2(a2+b2+c2)+ab+bc+caa+b+c\frac{b^2+c^2}{b+c}+\frac{a^2+b^2}{a+b}+\frac{c^2+a^2}{c+ a}\geq\frac{2(a^2+b^2+c^2)+ab+bc+ca}{a+b+c}
Preamble
import Mathlib.Analysis.Complex.Basic
Formal statement
theorem lean_workbook_plus_15933 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (b^2 + c^2) / (b + c) + (a^2 + b^2) / (a + b) + (c^2 + a^2) / (c + a) ≥ (2 * (a^2 + b^2 + c^2) + a * b + b * c + c * a) / (a + b + c)   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook

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