A cyclic rational sum of cubic differences is nonnegative

Proved

WorkbookSource.base_1727

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

lean-workbooksource-checked

Let $a, b, c>0$ . Prove that $\frac{a^3-b^3}{1+bc}+\frac{b^3-c ^3}{1+ca}+\frac{c^3-a^3}{1+ab}\ge 0$

Source: InternLM Lean-Workbook, record lean_workbook_1727 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_1727 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a^3 - b^3) / (1 + b * c) + (b^3 - c^3) / (1 + c * a) + (c^3 - a^3) / (1 + a * b) ≥ 0  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_1727; Apache-2.0

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