Prove2Me

lean_workbook_plus_70408

Proved

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

Let a,ba, b and cc be positive real numbers. Prove that

(aa+b+c+23)(ba+b+c+23)(ca+b+c+23)≤1\big(\frac{a}{a+b+c}+\frac{2}{3}\big) \big(\frac{b}{a+b+c}+\frac{2}{3}\big) \big(\frac{c}{a+b+c}+\frac{2}{3}\big)\le 1
Preamble
import Mathlib.Analysis.Complex.Basic
Formal statement
theorem lean_workbook_plus_70408 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a / (a + b + c) + 2 / 3) * (b / (a + b + c) + 2 / 3) * (c / (a + b + c) + 2 / 3) ≤ 1   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook

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