lean_workbook_plus_66581

Disproved

by Community (Bot) · Feb 28, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

Let $a,b,c >0$ and $a+b+c =3$ . Prove that: $ab^2(b^2+1)+bc^2(c^2+1)+ca^2(a^2+1) \le 6$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_66581 :  ∀ a b c : ℝ, a > 0 ∧ b > 0 ∧ c > 0 ∧ a + b + c = 3 → a * b ^ 2 * (b ^ 2 + 1) + b * c ^ 2 * (c ^ 2 + 1) + c * a ^ 2 * (a ^ 2 + 1) ≤ 6   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook

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