A mixed quadratic difference ratio sum upper bound

Proved

WorkbookSource.plus_9111

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

lean-workbooksource-checked

If $a,b,c > 0$ , then

$\frac {a^2 + b^2 - 3c^2}{a^2 + ab + b^2} + \frac {b^2 + c^2 - 3a^2}{b^2 + bc + c^2} + \frac {c^2 + a^2 - 3b^2}{c^2 + ca + a^2} + \frac {4}{3}\leq\frac {1}{3}$

Source: InternLM Lean-Workbook, record lean_workbook_plus_9111 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_9111 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a^2 + b^2 - 3*c^2)/(a^2 + a*b + b^2) + (b^2 + c^2 - 3*a^2)/(b^2 + b*c + c^2) + (c^2 + a^2 - 3*b^2)/(c^2 + c*a + a^2) + 4/3 ≤ 1/3   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_9111; Apache-2.0

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