A five-variable cyclic quadratic bound

Proved

WorkbookSource.base_52390

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

lean-workbooksource-checked

we only need to prove that: $5(a^{2}+b^{2}+c^{2}+d^{2}+e^{2})\le\ (a+b+c+d+e)^{2}+2\sum_{cyc}(3a-b-c-d)^{2}$

Source: InternLM Lean-Workbook, record lean_workbook_52390 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_52390 (a b c d e : ℝ) :
  5 * (a ^ 2 + b ^ 2 + c ^ 2 + d ^ 2 + e ^ 2) ≤
    (a + b + c + d + e) ^ 2 + 2 * ((3 * a - b - c - d) ^ 2 + (3 * b - c - d - e) ^ 2 + (3 * c - d - e - a) ^ 2 + (3 * d - e - a - b) ^ 2 + (3 * e - a - b - c) ^ 2)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_52390; Apache-2.0

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