A quartic norm bound with a cubic correction

Proved

WorkbookSource.base_28566

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

lean-workbooksource-checked

Let $a, b, c$ be positive real number such that $a+b+c=3$ . Prove that $7(a^2+b^2+c^2)^2+6abc\ge 23(a^2+b^2+c^2)$

Source: InternLM Lean-Workbook, record lean_workbook_28566 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_28566 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (habc : a + b + c = 3) : 7 * (a ^ 2 + b ^ 2 + c ^ 2) ^ 2 + 6 * a * b * c ≥ 23 * (a ^ 2 + b ^ 2 + c ^ 2)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_28566; Apache-2.0

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