A cyclic product comparison of quadratic and linear factors

Proved

WorkbookSource.base_53202

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

lean-workbooksource-checked

Let $a,b,c$ be positive real numbers . Prove that : $(a^2+b)(b^2+c)(c^2+a) \ge abc(a+1)(b+1)(c+1).$

Source: InternLM Lean-Workbook, record lean_workbook_53202 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_53202 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a^2 + b) * (b^2 + c) * (c^2 + a) ≥ a * b * c * (a + 1) * (b + 1) * (c + 1)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_53202; Apache-2.0

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