lean_workbook_plus_37670

Proved

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

Prove $a^2b^2 + b^2c^2 + c^2a^2 \geq abc(a + b + c)$ under the given condition $a,b,c > 0$ and $\frac {1} {a^2} + \frac {1} {b^2} + \frac {1} {c^2} = \frac {1} {2}$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_37670 :  ∀ a b c : ℝ, a > 0 ∧ b > 0 ∧ c > 0 ∧ 1 / a ^ 2 + 1 / b ^ 2 + 1 / c ^ 2 = 1 / 2 → a ^ 2 * b ^ 2 + b ^ 2 * c ^ 2 + c ^ 2 * a ^ 2 ≥ a * b * c * (a + b + c)   :=  by sorry

Source

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

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