A five-variable cyclic quadratic comparison

Proved

WorkbookSource.base_20107

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

lean-workbooksource-checked

If $a, b, c, d, e \ge 0$ , prove that $3\sum_{cyc}a^{2}+\sum_{cyc}ab \ge 4\sum_{cyc}ac$

Source: InternLM Lean-Workbook, record lean_workbook_20107 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_20107 {a b c d e : ℝ} (ha : 0 ≤ a) (hb : 0 ≤ b) (hc : 0 ≤ c) (hd : 0 ≤ d) (he : 0 ≤ e) : 3 * (a^2 + b^2 + c^2 + d^2 + e^2) + (a * b + b * c + c * d + d * e + e * a) ≥ 4 * (a * c + b * d + c * e + d * a + e * b)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_20107; Apache-2.0

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