A cyclic quadratic ratio comparison at fixed sum three

Proved

WorkbookSource.plus_55303

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

lean-workbooksource-checked

Let $a, b, c>0, a+b+c=3$ . Prove that $\frac{a^2}{b}+\frac{b^2}{c}+\frac{c^2}{a}\ge\frac{2a^2+b}{b+c+1}+\frac{2b^2+c}{c+a+1}+\frac{2c^2+a}{a+b+1}$

Source: InternLM Lean-Workbook, record lean_workbook_plus_55303 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_55303 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (habc : a + b + c = 3) : (a^2 / b + b^2 / c + c^2 / a) ≥ (2 * a^2 + b) / (b + c + 1) + (2 * b^2 + c) / (c + a + 1) + (2 * c^2 + a) / (a + b + 1)   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_55303; Apache-2.0

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