A five-variable difference of pairwise products

Proved

WorkbookSource.base_3361

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

lean-workbooksource-checked

Let $a,b,c,d, e \geq 0$ such that $a+b+c+d+e=5$ . Prove that: $ab+cd+ea +\frac{25}{4} \geq bc+de$

Source: InternLM Lean-Workbook, record lean_workbook_3361 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_3361 (a b c d e : ℝ) (ha : a ≥ 0) (hb : b ≥ 0) (hc : c ≥ 0) (hd : d ≥ 0) (he : e ≥ 0) (hab : a + b + c + d + e = 5) : a * b + c * d + e * a + 25 / 4 ≥ b * c + d * e  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_3361; Apache-2.0

View graph