A shifted cyclic cubic ratio sum is at least six

Proved

WorkbookSource.base_55115

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

lean-workbooksource-checked

Prove that for $a,b,c\in \mathbf{R^+}$ and $a+b+c=3$ , the following inequality holds: $\frac{a^3+5}{b+2}+\frac{b^3+5}{c+2}+\frac{c^3+5}{a+2}\geq 6$

Source: InternLM Lean-Workbook, record lean_workbook_55115 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_55115 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (habc : a + b + c = 3) : (a^3 + 5) / (b + 2) + (b^3 + 5) / (c + 2) + (c^3 + 5) / (a + 2) ≥ 6  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_55115; Apache-2.0

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