lean_workbook_plus_65176

Disproved

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

Let $a, b, c$ positive reals such that $0 \leq a, b, c \leq 1$ . Prove that \n\n $(a^2b + b^2c + c^2a)(ab^2 + bc^2 + ca^2)\geq (a^2 + b^2 + c^2 - 1)^2$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_65176 : ∀ a b c : ℝ, 0 ≤ a ∧ a ≤ 1 ∧ 0 ≤ b ∧ b ≤ 1 ∧ 0 ≤ c ∧ c ≤ 1 → (a^2 * b + b^2 * c + c^2 * a) * (a * b^2 + b * c^2 + c * a^2) ≥ (a^2 + b^2 + c^2 - 1)^2   :=  by sorry

Source

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

View graph