A five-variable cyclic product bound

Proved

WorkbookSource.base_7325

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

lean-workbooksource-checked

Given $a, b, c, d, e$ are real numbers such that $a + b + c + d + e = 1$ , prove that $2(ab + bc + cd + de + ea) + ac + bd + ce + da + eb \leq \frac{3}{5}$ .

Source: InternLM Lean-Workbook, record lean_workbook_7325 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_7325 (a b c d e : ℝ) (h : a + b + c + d + e = 1) :  2 * (a * b + b * c + c * d + d * e + e * a) + a * c + b * d + c * e + d * a + e * b ≤ 3 / 5  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_7325; Apache-2.0

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