Prove2Me

A cyclic squared difference ratio sum is at least three fifths

Proved
WorkbookSource.base_34416

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

lean-workbooksource-checked

If a,b,c>0 then (a−b+c)2a2+(b+c)2+(b−c+a)2b2+(c+a)2+(c−a+b)2c2+(a+b)2≥35 \frac {(a - b + c)^2}{a^2 + (b + c)^2} + \frac {(b - c + a)^2}{b^2 + (c + a)^2} + \frac {(c - a + b)^2}{c^2 + (a + b)^2} \ge \frac{3}{5} (Japan MO 2002)

Source: InternLM Lean-Workbook, record lean_workbook_34416 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble
import Mathlib
open Real Nat
Formal statement
theorem WorkbookSource.base_34416 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a - b + c) ^ 2 / (a ^ 2 + (b + c) ^ 2) + (b - c + a) ^ 2 / (b ^ 2 + (c + a) ^ 2) + (c - a + b) ^ 2 / (c ^ 2 + (a + b) ^ 2) ≥ 3 / 5  :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_34416; Apache-2.0

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