A cyclic quartic sum bounds a squared pairwise sum

Proved

WorkbookSource.plus_40403

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

lean-workbooksource-checked

If a, b, c are real number then: $a^4+b^4+c^4+a^3b+b^3c+c^3a\ge\frac{3}{5}(ab+bc+ca)^2$

Source: InternLM Lean-Workbook, record lean_workbook_plus_40403 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_40403 (a b c : ℝ) : a ^ 4 + b ^ 4 + c ^ 4 + a ^ 3 * b + b ^ 3 * c + c ^ 3 * a ≥ (3 / 5) * (a * b + b * c + c * a) ^ 2   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_40403; Apache-2.0

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