A four-variable triple-product-sum upper bound

Proved

WorkbookSource.plus_15874

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

lean-workbooksource-checked

Prove that for $a, b, c, d > 0$ and $a + b + c + d = 4$ , $abc + bcd + cda + dab \leq 4$ .

Source: InternLM Lean-Workbook, record lean_workbook_plus_15874 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_15874 (a b c d : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (hd : 0 < d) (hab : a + b + c + d = 4) : a * b * c + b * c * d + c * d * a + d * a * b ≤ 4   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_15874; Apache-2.0

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