A quartic norm bound with a cubic correction

Proved

WorkbookSource.base_37186

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

lean-workbooksource-checked

For non-negative $a,b,c$ such that $a+b+c=3$ prove that

(a^2+b^2+c^2)^2-2(a^3+b^3+c^3) \geq \frac{189}{64}

Source: InternLM Lean-Workbook, record lean_workbook_37186 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_37186 (a b c : ℝ) (ha : 0 ≤ a) (hb : 0 ≤ b) (hc : 0 ≤ c) (habc : a + b + c = 3) : (a^2 + b^2 + c^2)^2 - 2 * (a^3 + b^3 + c^3) ≥ 189 / 64  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_37186; Apache-2.0

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