Prove2Me

A fixed-sum quadratic reciprocal upper bound

Proved
WorkbookSource.base_368

by wamlart · Sep 13, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

Prove that a2a+2+b2b+2+c2c+2≤3ab+bc+ca\frac{a^2}{a+2}+\frac{b^2}{b+2}+\frac{c^2}{c+2} \leq \frac{3}{ab+bc+ca} given a,b,c>0a,b,c>0 and a+b+c=3a+b+c=3.

Source: InternLM Lean-Workbook, record lean_workbook_368 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble
import Mathlib
open Real Nat
Formal statement
theorem WorkbookSource.base_368 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (hab : a + b + c = 3) : (a^2 / (a + 2) + b^2 / (b + 2) + c^2 / (c + 2)) ≤ 3 / (a * b + b * c + a * c)  :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_368; Apache-2.0

View graph