A cyclic quartic bound involving two symmetric corrections

Proved

WorkbookSource.plus_73206

by wamlart · Sep 12, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

Prove that $(a^{2}+b^{2}+c^{2})^{2}+3(a^{2}b^{2}+b^{2}c^{2}+c^{2}a^{2})\geq 3(ab^{3}+bc^{3}+ca^{3})+3abc(a+b+c)$

Source: InternLM Lean-Workbook, record lean_workbook_plus_73206 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_73206 (a b c : ℝ) : (a ^ 2 + b ^ 2 + c ^ 2) ^ 2 + 3 * (a ^ 2 * b ^ 2 + b ^ 2 * c ^ 2 + c ^ 2 * a ^ 2) ≥ 3 * (a * b ^ 3 + b * c ^ 3 + c * a ^ 3) + 3 * a * b * c * (a + b + c)   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_73206; Apache-2.0

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