A six-variable cyclic inequality at zero sum

Proved

WorkbookSource.base_13609

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

lean-workbooksource-checked

prove $2(ab+bc+cd+de+ef+fa)\leq a^2+b^2+c^2+d^2+e^2+f^2$ given $a+b+c+d+e+f=0$

Source: InternLM Lean-Workbook, record lean_workbook_13609 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_13609 (a b c d e f : ℝ) (h : a + b + c + d + e + f = 0) :
  2 * (a * b + b * c + c * d + d * e + e * f + f * a) ≤ a ^ 2 + b ^ 2 + c ^ 2 + d ^ 2 + e ^ 2 + f ^ 2  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_13609; Apache-2.0

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