A five-variable cyclic triple-product-sum upper bound

Proved

WorkbookSource.plus_31693

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

lean-workbooksource-checked

Let $a,b,c,d,e$ be non-negative real numbers and $a+b+c+d+e=5$ . Prove: $abc+bcd+cde+dea+eab\le 5$

Source: InternLM Lean-Workbook, record lean_workbook_plus_31693 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_31693 (a b c d e : ℝ) (ha : 0 ≤ a) (hb : 0 ≤ b) (hc : 0 ≤ c) (hd : 0 ≤ d) (he : 0 ≤ e) (hab : a + b + c + d + e = 5) : a * b * c + b * c * d + c * d * e + d * e * a + e * a * b ≤ 5   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_31693; Apache-2.0

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