A normalized cubic sum with a cyclic correction

Proved

WorkbookSource.base_1132

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

lean-workbooksource-checked

Let $a,b,c>0$ . Prove that: $\frac{(a+b+c)^3}{3abc}+\frac{ab^2+bc^2+ca^2}{a^3+b^3+c^3} \geq 10$

Source: InternLM Lean-Workbook, record lean_workbook_1132 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_1132 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a + b + c) ^ 3 / (3 * a * b * c) + (a * b ^ 2 + b * c ^ 2 + c * a ^ 2) / (a ^ 3 + b ^ 3 + c ^ 3) ≥ 10  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_1132; Apache-2.0

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