Prove2Me

A cyclic squared pairwise ratio sum upper bound

Proved
WorkbookSource.plus_28300

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

lean-workbooksource-checked

The following inequality is true. Let a,b,c>0a, b, c>0 . Prove that (a+c)2(ab)(a+b)2+(a+b)2(bc)(c+b)2+(c+b)2(ca)(c+a)2≤(a+b+c)23\frac{(a+c)^2(ab)}{(a+b)^2}+\frac{(a+b)^2(bc)}{(c+b)^2}+\frac{(c+b)^2(ca)}{(c+a)^2} \leq \frac{(a+b+c)^2}{3}

Source: InternLM Lean-Workbook, record lean_workbook_plus_28300 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble
import Mathlib
open Real Nat
Formal statement
theorem WorkbookSource.plus_28300 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a + c) ^ 2 * a * b / (a + b) ^ 2 + (a + b) ^ 2 * b * c / (c + b) ^ 2 + (c + b) ^ 2 * c * a / (c + a) ^ 2 ≤ (a + b + c) ^ 2 / 3   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_28300; Apache-2.0

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