A cyclic quartic and quadratic upper bound at total three

Proved

WorkbookSource.base_30815

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

lean-workbooksource-checked

Let $a,b,c$ be real numbers such that $a+b+c=3.$ Prove that $3(a^3b+b^3c+c^3a)+16(ab+bc+ca) \leq 57.$

Source: InternLM Lean-Workbook, record lean_workbook_30815 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_30815 (a b c : ℝ) (h : a + b + c = 3) : 3 * (a ^ 3 * b + b ^ 3 * c + c ^ 3 * a) + 16 * (a * b + b * c + c * a) ≤ 57  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_30815; Apache-2.0

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