A quartic correction to a quadratic norm

Proved

WorkbookSource.base_41119

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

lean-workbooksource-checked

Let $a,b,c \ge 0$ such that $a+b+c=1$ . Prove that

a^2+b^2+c^2 \le \frac{3}{8}+ a^4+b^4+c^4

Source: InternLM Lean-Workbook, record lean_workbook_41119 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_41119 (a b c : ℝ) (ha : a ≥ 0) (hb : b ≥ 0) (hc : c ≥ 0)(habc : a + b + c = 1) : a^2 + b^2 + c^2 ≤ 3 / 8 + a^4 + b^4 + c^4  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_41119; Apache-2.0

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