A four-variable product inequality for nonnegative inputs

Proved

WorkbookSource.plus_18784

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

lean-workbooksource-checked

Prove or disprove: $(a+b+c)(b+c+d)(c+d+a)(d+a+b) \ge 4(a+b)(b+c)(c+d)(d+a)$ Given $a,b,c,d\ge 0$

Source: InternLM Lean-Workbook, record lean_workbook_plus_18784 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_18784 {a b c d : ℝ} (ha : a ≥ 0) (hb : b ≥ 0) (hc : c ≥ 0) (hd : d ≥ 0) : (a + b + c) * (b + c + d) * (c + d + a) * (d + a + b) ≥ 4 * (a + b) * (b + c) * (c + d) * (d + a)   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_18784; Apache-2.0

View graph