A strengthened product inequality for three quadratic factors

Proved

WorkbookSource.base_13717

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

lean-workbooksource-checked

The inequality

2(a^2+1)(b^2+1)(c^2+1) \ge (a+1)(b+1)(c+1)(a+b+c-1)+2(abc-1)^2,

is also true for all $a,\,b,\,c$ are real numbers.

Source: InternLM Lean-Workbook, record lean_workbook_13717 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_13717 (a b c : ℝ) : 2 * (a ^ 2 + 1) * (b ^ 2 + 1) * (c ^ 2 + 1) ≥ (a + 1) * (b + 1) * (c + 1) * (a + b + c - 1) + 2 * (a * b * c - 1) ^ 2  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_13717; Apache-2.0

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