A cyclic cubic bound at fixed squared norm

Proved

WorkbookSource.base_17945

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

lean-workbooksource-checked

Let $a,b,c$ be nonnegative real numbers such that $a^2+b^2+c^2=3$ . Prove that $a^2b+b^2c+c^2a \leq a+b+c$

Source: InternLM Lean-Workbook, record lean_workbook_17945 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_17945 (a b c : ℝ) (ha : 0 ≤ a) (hb : 0 ≤ b) (hc : 0 ≤ c) (hab : a^2 + b^2 + c^2 = 3) : a^2 * b + b^2 * c + c^2 * a ≤ a + b + c  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_17945; Apache-2.0

View graph