A cyclic cubic inequality with coefficient four

Proved

WorkbookSource.base_34828

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

lean-workbooksource-checked

Prove that for any positive real numbers $a$ , $b$ , and $c$ , the inequality $3(a^3+b^3+c^3+abc) \geq 4(a^2b+b^2c+c^2a)$ holds.

Source: InternLM Lean-Workbook, record lean_workbook_34828 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_34828 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : 3 * (a^3 + b^3 + c^3 + a * b * c) ≥ 4 * (a^2 * b + b^2 * c + c^2 * a)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_34828; Apache-2.0

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