A cyclic quadratic-product ratio sum bounds the total

Proved

WorkbookSource.base_6752

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

lean-workbooksource-checked

Let $a$ , $b$ and $c$ be positive numbers. Prove that

\frac{a^2(b+c)}{b^2+c^2}+\frac{b^2(c+a)}{c^2+a^2}+\frac{c^2(a+b)}{a^2+b^2}\geq a+b+c

Source: InternLM Lean-Workbook, record lean_workbook_6752 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_6752 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a^2 * (b + c) / (b^2 + c^2) + b^2 * (c + a) / (c^2 + a^2) + c^2 * (a + b) / (a^2 + b^2)) ≥ a + b + c  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_6752; Apache-2.0

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