A product inequality involving the elementary symmetric sums

Proved

WorkbookSource.base_43488

by wamlart · Sep 12, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

Prove that $(a^2+1)(b^2+1)(c^2+1)+8abc\ge (a+b+c+abc)(1+ab+bc+ca)$ for all real $a, b, c$ .

Source: InternLM Lean-Workbook, record lean_workbook_43488 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_43488 (a b c : ℝ) : (a ^ 2 + 1) * (b ^ 2 + 1) * (c ^ 2 + 1) + 8 * a * b * c ≥ (a + b + c + a * b * c) * (1 + a * b + b * c + c * a)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_43488; Apache-2.0

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