A cyclic quartic inequality with asymmetric coefficients

Proved

WorkbookSource.base_36056

by wamlart · Sep 12, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

For positive real numbers $a, b, c$ prove the inequality

a^3b+b^3c+c^3a+4(ab^3+bc^3+ca^3)\geq 4(a^2b^2+b^2c^2+c^2a^2)+abc(a+b+c)

Source: InternLM Lean-Workbook, record lean_workbook_36056 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_36056 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : a^3 * b + b^3 * c + c^3 * a + 4 * (a * b^3 + b * c^3 + c * a^3) ≥ 4 * (a^2 * b^2 + b^2 * c^2 + c^2 * a^2) + a * b * c * (a + b + c)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_36056; Apache-2.0

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