Prove2Me

A cubic ratio bounds a normalized total cube

Proved
WorkbookSource.plus_18904

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

lean-workbooksource-checked

Let a,b,ca,b,c be positive real numbers.Prove that a3+b3+c3abc≥89⋅(a+b+c)3(b+c)(c+a)(a+b).{ \frac{a^3+b^3+c^3}{abc}\geq \frac{8}{9}\cdot \frac{(a+b+c)^3}{(b+c)(c+a)(a+b)}} .

Source: InternLM Lean-Workbook, record lean_workbook_plus_18904 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble
import Mathlib
open Real Nat
Formal statement
theorem WorkbookSource.plus_18904 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a^3 + b^3 + c^3) / (a * b * c) ≥ (8 / 9) * (a + b + c)^3 / ((b + c) * (c + a) * (a + b))   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_18904; Apache-2.0

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