A shifted cyclic quadratic ratio lower bound at fixed sum six

Proved

WorkbookSource.base_44851

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

lean-workbooksource-checked

Let $a,$ $b$ and $c$ are positive numbers such that $a+b+c=6.$ Prove that $\frac{a}{b^2+c}+\frac{b}{c^2+a}+\frac{c}{a^2+b}\geq1$

Source: InternLM Lean-Workbook, record lean_workbook_44851 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_44851 (a b c : ℝ) (ha : a > 0) (hb : b > 0) (hc : c > 0) (habc : a + b + c = 6) : a / (b * b + c) + b / (c * c + a) + c / (a * a + b) ≥ 1  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_44851; Apache-2.0

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