A cyclic quartic inequality with a shifted squared sum

Proved

WorkbookSource.base_43398

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

lean-workbooksource-checked

Prove that $(a^{2}+b^{2}+c^{2}-1)^{2} \geq 2(a^{3}b+b^{3}c+c^{3}a-1)$ for any $a,b,c \geq 0$ .

Source: InternLM Lean-Workbook, record lean_workbook_43398 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_43398 (a b c : ℝ) (ha : a ≥ 0) (hb : b ≥ 0) (hc : c ≥ 0) : (a^2 + b^2 + c^2 - 1)^2 ≥ 2 * (a^3 * b + b^3 * c + c^3 * a - 1)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_43398; Apache-2.0

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