A pairwise cubic-over-quadratic sum bounds the total

Proved

WorkbookSource.base_16260

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

lean-workbooksource-checked

For $a,b,c>0$ . Prove that: $\frac{a^3+b^3}{a^2+b^2}+\frac{b^3+c^3}{b^2+c^2}+\frac{c^3+a^3}{c^2+a^2}\ge a+b+c$

Source: InternLM Lean-Workbook, record lean_workbook_16260 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_16260 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a^3 + b^3) / (a^2 + b^2) + (b^3 + c^3) / (b^2 + c^2) + (c^3 + a^3) / (c^2 + a^2) ≥ a + b + c  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_16260; Apache-2.0

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