Prove2Me

A quartic bound for symmetric cubic products

Proved
WorkbookSource.base_46897

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

lean-workbooksource-checked

Prove that 9∑a3(b+c)+3∑a2bc≤4∑a4+17∑a2b29\sum a^{3}(b+c)+3\sum a^{2}bc \le 4\sum a^{4}+17\sum a^{2}b^{2}

Source: InternLM Lean-Workbook, record lean_workbook_46897 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble
import Mathlib
open Real Nat
Formal statement
theorem WorkbookSource.base_46897 (a b c : ℝ) : 9 * (a ^ 3 * (b + c) + b ^ 3 * (c + a) + c ^ 3 * (a + b)) + 3 * (a ^ 2 * b * c + b ^ 2 * c * a + c ^ 2 * a * b) ≤ 4 * (a ^ 4 + b ^ 4 + c ^ 4) + 17 * (a ^ 2 * b ^ 2 + b ^ 2 * c ^ 2 + c ^ 2 * a ^ 2)  :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_46897; Apache-2.0

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