A sum-of-squares bound from a quartic and product constraint

Proved

WorkbookCorrected.plus_32112

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

corrected-formalizationlean-workbooksource-checked

Let $a,b,c$ be non-negative real numbers such that $a^4+b^4+c^4+abc=4$ . Prove that: $a^2+b^2+c^2 \leq 3$

Formalization Note: The original formalization added abc=1, which is absent from the source. This correction removes that extra assumption and proves the entire source proposition for nonnegative real variables.

Source: InternLM Lean-Workbook, record lean_workbook_plus_32112 (Apache-2.0).

Preamble

import Mathlib

Formal statement

theorem WorkbookCorrected.plus_32112 (a b c : ℝ) (ha : 0 ≤ a) (hb : 0 ≤ b) (hc : 0 ≤ c)
    (h : a^4+b^4+c^4+a*b*c=4) : a^2+b^2+c^2 ≤ 3 := by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_32112; Apache-2.0

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