A cyclic quadratic ratio bound at fixed sum three

Proved

WorkbookSource.base_1835

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

lean-workbooksource-checked

Let $a,b,c>0$ and $a+b+c=3$ . Prove

$\sum_{cyc} \frac{a^2}{a+b^2}\geq \frac{3}{2}$

Source: InternLM Lean-Workbook, record lean_workbook_1835 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_1835 (a b c : ℝ) (ha : a > 0) (hb : b > 0) (hc : c > 0) (hab : a + b + c = 3) : (a^2 / (a + b^2) + b^2 / (b + c^2) + c^2 / (c + a^2)) ≥ 3 / 2  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_1835; Apache-2.0

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