Prove2Me

A symmetric squared difference ratio sum is at least one half

Proved
WorkbookSource.base_16015

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

lean-workbooksource-checked

Prove that if a,b,c>0a,b,c>0 then

(a+b−3c)22c2+(a+b)2+(c+a−3b)22b2+(c+a)2+(b+c−3a)22a2+(b+c)2≥12.\frac{(a+b-3c)^2}{2c^2+(a+b)^2}+\frac{(c+a-3b)^2}{2b^2+(c+a)^2}+\frac{(b+c-3a)^2}{2a^2+(b+c)^2}\geq \frac12.

Source: InternLM Lean-Workbook, record lean_workbook_16015 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble
import Mathlib
open Real Nat
Formal statement
theorem WorkbookSource.base_16015 (a b c : ℝ) (ha : a > 0) (hb : b > 0) (hc : c > 0) : (a + b - 3 * c) ^ 2 / (2 * c ^ 2 + (a + b) ^ 2) + (c + a - 3 * b) ^ 2 / (2 * b ^ 2 + (c + a) ^ 2) + (b + c - 3 * a) ^ 2 / (2 * a ^ 2 + (b + c) ^ 2) ≥ 1 / 2  :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_16015; Apache-2.0

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