A shifted cyclic cubic ratio sum bounds the total

Proved

WorkbookSource.base_22723

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

lean-workbooksource-checked

If $a, b, c>0$ prove that $\frac{a+b^3}{b^2+1}+\frac{b+c^3}{c^2+1}+\frac{c+a^3}{a^2+1}\ge a+b+c$

Source: InternLM Lean-Workbook, record lean_workbook_22723 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_22723 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a + b^3) / (b^2 + 1) + (b + c^3) / (c^2 + 1) + (c + a^3) / (a^2 + 1) ≥ a + b + c  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_22723; Apache-2.0

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