A cyclic linear ratio upper bound at fixed sum three

Proved

WorkbookSource.base_37298

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

lean-workbooksource-checked

Let positive reals $a,b,c$ which satisfy: $a+b+c=3$ Prove that: $\frac{2a}{a+b}+\frac{2b}{b+c}+\frac{2c}{c+a} \le a^2+b^2+c^2$

Source: InternLM Lean-Workbook, record lean_workbook_37298 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_37298 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (hab : a + b + c = 3) : (2 * a / (a + b) + 2 * b / (b + c) + 2 * c / (c + a)) ≤ a ^ 2 + b ^ 2 + c ^ 2  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_37298; Apache-2.0

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