Prove2Me

A bound for pairwise cubic products and triangle factors

Proved
WorkbookSource.base_5136

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

lean-workbooksource-checked

Let a,b,c>0 Prove that ∑a3b3≥(−a+b+c)(a−b+c)(a+b−c)(a3+b3+c3) \sum a^3b^3 \geq (-a+b+c)(a-b+c)(a+b-c)(a^3+b^3+c^3)

Source: InternLM Lean-Workbook, record lean_workbook_5136 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble
import Mathlib
open Real Nat
Formal statement
theorem WorkbookSource.base_5136 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : a^3 * b^3 + b^3 * c^3 + c^3 * a^3 ≥ (-a + b + c) * (a - b + c) * (a + b - c) * (a^3 + b^3 + c^3)  :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_5136; Apache-2.0

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