A shifted cubic ratio sum is at least three

Proved

WorkbookSource.plus_11598

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

lean-workbooksource-checked

With the conditions of $a+b+c=3$ and $a,b,c>0$ , Prove that $\sum _{cyc} \frac{a^3+1}{a^2+1} \ge 3$

Source: InternLM Lean-Workbook, record lean_workbook_plus_11598 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_11598 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (hab : a + b + c = 3) : (a^3 + 1)/(a^2 + 1) + (b^3 + 1)/(b^2 + 1) + (c^3 + 1)/(c^2 + 1) ≥ 3   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_11598; Apache-2.0

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