A six-variable cyclic triple-product bound

Proved

WorkbookSource.base_15025

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

lean-workbooksource-checked

If some reals $a > 0$ , $b > 0$ , $c > 0$ , $d > 0$ , $e > 0$ , $f > 0$ satisfy $a + b + c + d + e + f = 1$ , then prove that $abc + bcd + cde + def + efa + fab\leq\frac {1}{27}$ .

Source: InternLM Lean-Workbook, record lean_workbook_15025 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_15025 (a b c d e f : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (hd : 0 < d) (he : 0 < e) (hf : 0 < f) (habcdef : a + b + c + d + e + f = 1) : a * b * c + b * c * d + c * d * e + d * e * f + e * f * a + f * a * b ≤ 1 / 27  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_15025; Apache-2.0

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