A cyclic cubic sum is at most four at total three

Proved

WorkbookSource.base_12079

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

lean-workbooksource-checked

If $a$ , $b$ , $c$ are nonnegative reals such that $a + b + c = 3$ , then prove that: $a^2b + b^2c + c^2a\leq 4$ .

Source: InternLM Lean-Workbook, record lean_workbook_12079 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_12079 (a b c : ℝ) (ha : 0 ≤ a) (hb : 0 ≤ b) (hc : 0 ≤ c) (hab : a + b + c = 3) : a^2 * b + b^2 * c + c^2 * a ≤ 4  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_12079; Apache-2.0

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