A cyclic quartic ratio sum is at least three halves

Proved

WorkbookSource.plus_52739

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

lean-workbooksource-checked

For positive $a,\ b,\ c$ , such that $a+b+c=3$ Prove that : $\sum \frac{a^4}{b^2+c}\ge \frac{3}{2}$

Source: InternLM Lean-Workbook, record lean_workbook_plus_52739 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_52739 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (habc : a + b + c = 3) : a^4 / (b^2 + c) + b^4 / (c^2 + a) + c^4 / (a^2 + b) ≥ 3 / 2   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_52739; Apache-2.0

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