Prove2Me

lean_workbook_plus_13190

Disproved

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

Prove that (a+b+c)2a+b+c+ab+bc+ca≥3(a+b+c)23(a+b+c)+(a+b+c)2=3(a+b+c)a+b+c+3\dfrac{(a+b+c)^2}{a+b+c+ab+bc+ca} \geq \dfrac{3(a+b+c)^2}{3(a+b+c)+(a+b+c)^2}=\dfrac{3(a+b+c)}{a+b+c+3}

Preamble
import Mathlib.Analysis.Complex.Basic
Formal statement
theorem lean_workbook_plus_13190 : ∀ a b c : ℝ, (a + b + c) ^ 2 / (a + b + c + a * b + b * c + c * a) ≥ 3 * (a + b + c) ^ 2 / (3 * (a + b + c) + (a + b + c) ^ 2)   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook

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