A quartic-cubic-quadratic power-sum inequality at total one

Proved

WorkbookSource.base_12796

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

lean-workbooksource-checked

If $a,b,c$ be real numbers such that $a+b+c=1$ , then $1+18\sum a^4+6\sum a^2 \ge 24\sum a^3$ .

Source: InternLM Lean-Workbook, record lean_workbook_12796 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_12796 (a b c : ℝ) (habc : a + b + c = 1) : 1 + 18 * (a ^ 4 + b ^ 4 + c ^ 4) + 6 * (a ^ 2 + b ^ 2 + c ^ 2) ≥ 24 * (a ^ 3 + b ^ 3 + c ^ 3)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_12796; Apache-2.0

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