Prove2Me

A cyclic squared ratio sum with a triple-product correction

Proved
WorkbookSource.base_10043

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

lean-workbooksource-checked

Prove that if a,b,c>0, then: a2(a+b)2+b2(b+c)2+c2(c+a)2+2abc(b+c)(c+a)(a+b) \frac{a^2}{(a+b)^2}+\frac{b^2}{(b+c)^2}+\frac{c^2}{(c+a)^2}+\frac{2abc}{(b+c)(c+a)(a+b)} ≥1

Source: InternLM Lean-Workbook, record lean_workbook_10043 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble
import Mathlib
open Real Nat
Formal statement
theorem WorkbookSource.base_10043 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a^2 / (a + b)^2 + b^2 / (b + c)^2 + c^2 / (c + a)^2 + (2 * a * b * c) / ((b + c) * (c + a) * (a + b))) ≥ 1  :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_10043; Apache-2.0

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