A product of shifted linear factors bounds mixed products

Proved

WorkbookSource.base_50368

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

lean-workbooksource-checked

Given $a, b, c \geq 0$ , prove that $(a+b+c+1)(a+1)(b+1)(c+1) \geq 8(ab+bc+ca+abc)$ .

Source: InternLM Lean-Workbook, record lean_workbook_50368 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_50368 (a b c : ℝ) (ha : a ≥ 0) (hb : b ≥ 0) (hc : c ≥ 0) : (a + b + c + 1) * (a + 1) * (b + 1) * (c + 1) ≥ 8 * (a * b + b * c + c * a + a * b * c)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_50368; Apache-2.0

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