A fourth-degree bound for variables of sum two

Proved

WorkbookSource.base_3985

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

lean-workbooksource-checked

Let a,b,c be non-negative real numbers with sum 2. Prove that: $24(a^2+b^2+c^2)+(a^2+b^2+c^2)^2 \le 48+8(a^3+b^3+c^3)$

Source: InternLM Lean-Workbook, record lean_workbook_3985 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_3985 (a b c : ℝ) (ha : 0 ≤ a) (hb : 0 ≤ b) (hc : 0 ≤ c) (habc : a + b + c = 2) : 24 * (a ^ 2 + b ^ 2 + c ^ 2) + (a ^ 2 + b ^ 2 + c ^ 2) ^ 2 ≤ 48 + 8 * (a ^ 3 + b ^ 3 + c ^ 3)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_3985; Apache-2.0

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